import Pretty.Supports.ResolvePareto
import Pretty.Supports.DocSize
import Pretty.Supports.MeasRender
import Pretty.Claims.Widen

/-!
## Validity theorems
-/

mutual 
  /--
  The validity theorem for non-tainted result (the first part of Theorem 5.8)
  -/
  theorem 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid (
h_print: Resolve F d c i (MeasureSet.set ms h)
h_print : 
Resolve: {α : Type} → Factory α → Doc → ℕ → ℕ → MeasureSet → Prop
Resolve 
F: ?m.4
F 
d: ?m.11
d 
c: ?m.17
c 
i: ?m.23
i (
MeasureSet.set: {α : Type} → (ms : List Meas) → ms ≠ [] → MeasureSet
MeasureSet.set 
ms: ?m.32
ms 
h: ?m.41
h))
      (
h_widen: Widen d D
h_widen : 
Widen: Doc → List Doc → Prop
Widen 
d: ?m.11
d 
D: ?m.54
D) (
h_m: m ∈ ms
h_m : 
m: ?m.81
m ∈ 
ms: ?m.32
ms) : ∃ 
d_choiceless: ?m.123
d_choiceless, 
d_choiceless: ?m.123
d_choiceless ∈ 
D: ?m.54
D ∧ 
      
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: ?m.4
F 
d_choiceless: ?m.123
d_choiceless 
c: ?m.17
c 
i: ?m.23
i 
m: ?m.81
m := by
Goals accomplished! 🐙 
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mmatch 
d: Doc
d with
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.text: String → Doc
Doc.text 
s: String
s =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

s: String

h_print: Resolve F (Doc.text s) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.text s) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F (Doc.text s) c i (MeasureSet.set ms h)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

s: String

h_widen: Widen (Doc.text s) D

m✝: Meas

h_c✝: c + String.length s ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F (Doc.text s) c i m✝

h: [m✝] ≠ []

h_m: m ∈ [m✝]

text_set
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

s: String

h_print: Resolve F (Doc.text s) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.text s) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
List.eq_of_mem_singleton: ∀ {α : Type ?u.1509} {a b : α}, a ∈ [b] → a = b
List.eq_of_mem_singleton 
h_m: m ∈ [m✝]
h_m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

s: String

h_widen: Widen (Doc.text s) D

h_c✝: c + String.length s ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F (Doc.text s) c i m

h: [m] ≠ []

h_m: m ∈ [m]

text_set.refl
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

s: String

h_print: Resolve F (Doc.text s) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.text s) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mexists 
Doc.text: String → Doc
Doc.text 
s: String
s
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

s: String

h_widen: Widen (Doc.text s) D

h_c✝: c + String.length s ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F (Doc.text s) c i m

h: [m] ≠ []

h_m: m ∈ [m]

text_set.refl
Doc.text s ∈ D ∧ MeasRender F (Doc.text s) c i m
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

s: String

h_print: Resolve F (Doc.text s) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.text s) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mconstructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

s: String

h_widen: Widen (Doc.text s) D

h_c✝: c + String.length s ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F (Doc.text s) c i m

h: [m] ≠ []

h_m: m ∈ [m]

text_set.refl.left
Doc.text s ∈ D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

s: String

h_widen: Widen (Doc.text s) D

h_c✝: c + String.length s ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F (Doc.text s) c i m

h: [m] ≠ []

h_m: m ∈ [m]

text_set.refl.right
MeasRender F (Doc.text s) c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

s: String

h_print: Resolve F (Doc.text s) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.text s) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase left => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

s: String

h_widen: Widen (Doc.text s) D

h_c✝: c + String.length s ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F (Doc.text s) c i m

h: [m] ≠ []

h_m: m ∈ [m]

Doc.text s ∈ Dcases 
h_widen: Widen (Doc.text s) D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

s: String

h_c✝: c + String.length s ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F (Doc.text s) c i m

h: [m] ≠ []

h_m: m ∈ [m]

text
Doc.text s ∈ [Doc.text s] 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

s: String

h_widen: Widen (Doc.text s) D

h_c✝: c + String.length s ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F (Doc.text s) c i m

h: [m] ≠ []

h_m: m ∈ [m]

Doc.text s ∈ Dsimp
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

s: String

h_print: Resolve F (Doc.text s) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.text s) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase right => 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

s: String

h_widen: Widen (Doc.text s) D

h_c✝: c + String.length s ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F (Doc.text s) c i m

h: [m] ≠ []

h_m: m ∈ [m]

MeasRender F (Doc.text s) c i massumption
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.nl: Doc
Doc.nl =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

h_print: Resolve F Doc.nl c i (MeasureSet.set ms h)

h_widen: Widen Doc.nl D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F Doc.nl c i (MeasureSet.set ms h)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

h_widen: Widen Doc.nl D

m✝: Meas

h_c✝: c ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F Doc.nl c i m✝

h: [m✝] ≠ []

h_m: m ∈ [m✝]

line_set
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

h_print: Resolve F Doc.nl c i (MeasureSet.set ms h)

h_widen: Widen Doc.nl D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
List.eq_of_mem_singleton: ∀ {α : Type ?u.3921} {a b : α}, a ∈ [b] → a = b
List.eq_of_mem_singleton 
h_m: m ∈ [m✝]
h_m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

h_widen: Widen Doc.nl D

h_c✝: c ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F Doc.nl c i m

h: [m] ≠ []

h_m: m ∈ [m]

line_set.refl
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

h_print: Resolve F Doc.nl c i (MeasureSet.set ms h)

h_widen: Widen Doc.nl D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mexists 
Doc.nl: Doc
Doc.nl
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

h_widen: Widen Doc.nl D

h_c✝: c ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F Doc.nl c i m

h: [m] ≠ []

h_m: m ∈ [m]

line_set.refl
Doc.nl ∈ D ∧ MeasRender F Doc.nl c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

h_print: Resolve F Doc.nl c i (MeasureSet.set ms h)

h_widen: Widen Doc.nl D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mconstructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

h_widen: Widen Doc.nl D

h_c✝: c ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F Doc.nl c i m

h: [m] ≠ []

h_m: m ∈ [m]

line_set.refl.left
Doc.nl ∈ D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

h_widen: Widen Doc.nl D

h_c✝: c ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F Doc.nl c i m

h: [m] ≠ []

h_m: m ∈ [m]

line_set.refl.right
MeasRender F Doc.nl c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

h_print: Resolve F Doc.nl c i (MeasureSet.set ms h)

h_widen: Widen Doc.nl D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase left => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

h_widen: Widen Doc.nl D

h_c✝: c ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F Doc.nl c i m

h: [m] ≠ []

h_m: m ∈ [m]

Doc.nl ∈ Dcases 
h_widen: Widen Doc.nl D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_c✝: c ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F Doc.nl c i m

h: [m] ≠ []

h_m: m ∈ [m]

nl
Doc.nl ∈ [Doc.nl] 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

h_widen: Widen Doc.nl D

h_c✝: c ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F Doc.nl c i m

h: [m] ≠ []

h_m: m ∈ [m]

Doc.nl ∈ Dsimp
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

h_print: Resolve F Doc.nl c i (MeasureSet.set ms h)

h_widen: Widen Doc.nl D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase right => 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

h_widen: Widen Doc.nl D

h_c✝: c ≤ F.W

h_i✝: i ≤ F.W

h✝: MeasRender F Doc.nl c i m

h: [m] ≠ []

h_m: m ∈ [m]

MeasRender F Doc.nl c i massumption
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.nest: ℕ → Doc → Doc
Doc.nest 
n: ℕ
n 
d': Doc
d' =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_print: Resolve F (Doc.nest n d') c i (MeasureSet.set ms h)

h_widen: Widen (Doc.nest n d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mgeneralize h_gen : 
MeasureSet.set: {α : Type} → (ms : List Meas) → ms ≠ [] → MeasureSet
MeasureSet.set 
_: List Meas
_ 
_: ?m.6488 ≠ []
_ = ms at 
h_print: Resolve F (Doc.nest n d') c i (MeasureSet.set ms h)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms✝: List Meas

h: ms✝ ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms✝

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms: MeasureSet

h_gen: MeasureSet.set ms✝ h = ms

h_print: Resolve F (Doc.nest n d') c i ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_print: Resolve F (Doc.nest n d') c i (MeasureSet.set ms h)

h_widen: Widen (Doc.nest n d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F (Doc.nest n d') c i ms
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms✝: MeasureSet

h✝: Resolve F d' c (i + n) ms✝

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) ms✝

nest
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_print: Resolve F (Doc.nest n d') c i (MeasureSet.set ms h)

h_widen: Widen (Doc.nest n d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase nest 
ms': MeasureSet
ms' 
h': Resolve F d' c (i + n) ms'
h' => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms': MeasureSet

h': Resolve F d' c (i + n) ms'

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
ms': MeasureSet
ms'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

tainted
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms': MeasureSet

h': Resolve F d' c (i + n) ms'

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase tainted => 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift] at 
h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)
h_gen
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms': MeasureSet

h': Resolve F d' c (i + n) ms'

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase set => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift] at 
h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set ms✝ h✝)
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h_gen: ms = List.map (Meas.adjust_nest n) ms✝

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msubst 
h_gen: ms = List.map (Meas.adjust_nest n) ms✝
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_widen: Widen (Doc.nest n d') D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝¹: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝¹)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

L✝: List Doc

h✝: Widen d' L✝

nest
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase nest 
h_widen: Widen d' L✝
h_widen => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i msimp at 
h_m: m ∈ List.map (Meas.adjust_nest n) ms✝
h_m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d' L✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_nest n a = m

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i mlet ⟨
m': Meas
m', ⟨
h_left: m' ∈ ms✝
h_left, 
h_right: Meas.adjust_nest n m' = m
h_right⟩⟩ := 
h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_nest n a = m
h_m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d' L✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_nest n a = m

m': Meas

h_left: m' ∈ ms✝

h_right: Meas.adjust_nest n m' = m

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i m 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i mlet ⟨
d': Doc
d', 
h_in: d' ∈ L✝
h_in, 
h_render: MeasRender F d' c (i + n) m'
h_render⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)
h' 
h_widen: Widen d' L✝
h_widen 
h_left: m' ∈ ms✝
h_left
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d'✝: Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d'✝ c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d'✝ L✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_nest n a = m

m': Meas

h_left: m' ∈ ms✝

h_right: Meas.adjust_nest n m' = m

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c (i + n) m'

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i mexists 
Doc.nest: ℕ → Doc → Doc
Doc.nest 
n: ℕ
n 
d': Doc
d'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d'✝: Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d'✝ c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d'✝ L✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_nest n a = m

m': Meas

h_left: m' ∈ ms✝

h_right: Meas.adjust_nest n m' = m

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c (i + n) m'

Doc.nest n d' ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F (Doc.nest n d') c i m 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i msimp [*]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d'✝: Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d'✝ c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d'✝ L✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_nest n a = m

m': Meas

h_left: m' ∈ ms✝

h_right: Meas.adjust_nest n m' = m

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c (i + n) m'

MeasRender F (Doc.nest n d') c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i msubst 
h_right: Meas.adjust_nest n m' = m
h_right
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d'✝: Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d'✝ c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d'✝ L✝

m': Meas

h_left: m' ∈ ms✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c (i + n) m'

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_nest n a = Meas.adjust_nest n m'

MeasRender F (Doc.nest n d') c i (Meas.adjust_nest n m') 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i mhave := 
MeasRender_doc: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas}, MeasRender F d c i m → Choiceless d → m.doc = d
MeasRender_doc 
h_render: MeasRender F d' c (i + n) m'
h_render (
Widen_choiceless: ∀ {d : Doc} {D : List Doc} {d_choiceless : Doc}, Widen d D → d_choiceless ∈ D → Choiceless d_choiceless
Widen_choiceless 
h_widen: Widen d'✝ L✝
h_widen 
h_in: d' ∈ L✝
h_in)
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d'✝: Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d'✝ c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d'✝ L✝

m': Meas

h_left: m' ∈ ms✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c (i + n) m'

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_nest n a = Meas.adjust_nest n m'

this: m'.doc = d'

MeasRender F (Doc.nest n d') c i (Meas.adjust_nest n m')
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i msubst 
this: ?m.14055
this
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d' L✝

m': Meas

h_left: m' ∈ ms✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_nest n a = Meas.adjust_nest n m'

h_in: m'.doc ∈ L✝

h_render: MeasRender F m'.doc c (i + n) m'

MeasRender F (Doc.nest n m'.doc) c i (Meas.adjust_nest n m') 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i mconstructor
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d' L✝

m': Meas

h_left: m' ∈ ms✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_nest n a = Meas.adjust_nest n m'

h_in: m'.doc ∈ L✝

h_render: MeasRender F m'.doc c (i + n) m'

h
MeasRender F m'.doc c (i + n)
  { last := (Meas.adjust_nest n m').last, cost := (Meas.adjust_nest n m').cost, doc := m'.doc,
    x := (Meas.adjust_nest n m').x, y := (Meas.adjust_nest n m').y }
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

n: ℕ

d': Doc

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_nest n) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_nest n) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i msimpa [
Meas.adjust_nest: {α : Type} → ℕ → Meas → Meas
Meas.adjust_nest]
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.align: Doc → Doc
Doc.align 
d': Doc
d' =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_print: Resolve F (Doc.align d') c i (MeasureSet.set ms h)

h_widen: Widen (Doc.align d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mgeneralize h_gen : 
MeasureSet.set: {α : Type} → (ms : List Meas) → ms ≠ [] → MeasureSet
MeasureSet.set 
_: List Meas
_ 
_: ?m.14241 ≠ []
_ = ms at 
h_print: Resolve F (Doc.align d') c i (MeasureSet.set ms h)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms✝: List Meas

h: ms✝ ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms✝

d': Doc

h_widen: Widen (Doc.align d') D

ms: MeasureSet

h_gen: MeasureSet.set ms✝ h = ms

h_print: Resolve F (Doc.align d') c i ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_print: Resolve F (Doc.align d') c i (MeasureSet.set ms h)

h_widen: Widen (Doc.align d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F (Doc.align d') c i ms
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

ms✝: MeasureSet

h✝: Resolve F d' c c ms✝

h_bad✝: i > F.W

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms✝)

align_taint
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

ms✝: MeasureSet

h✝: Resolve F d' c c ms✝

h_ok✝: i ≤ F.W

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) ms✝

align
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_print: Resolve F (Doc.align d') c i (MeasureSet.set ms h)

h_widen: Widen (Doc.align d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase align 
ms': MeasureSet
ms' 
h': Resolve F d' c c ms'
h' _ => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h': Resolve F d' c c ms'

h_ok✝: i ≤ F.W

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
ms': MeasureSet
ms'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

tainted
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h': Resolve F d' c c ms'

h_ok✝: i ≤ F.W

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase tainted => 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift] at 
h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)
h_gen
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h': Resolve F d' c c ms'

h_ok✝: i ≤ F.W

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase set => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift] at 
h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set ms✝ h✝)
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h_gen: ms = List.map (Meas.adjust_align i) ms✝

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msubst 
h_gen: ms = List.map (Meas.adjust_align i) ms✝
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

m: Meas

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_widen: Widen (Doc.align d') D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝¹: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝¹)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

L✝: List Doc

h✝: Widen d' L✝

align
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase align 
h_widen: Widen d' L✝
h_widen => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i msimp at 
h_m: m ∈ List.map (Meas.adjust_align i) ms✝
h_m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d' L✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_align i a = m

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i mlet ⟨
m': Meas
m', ⟨
h_left: m' ∈ ms✝
h_left, 
h_right: Meas.adjust_align i m' = m
h_right⟩⟩ := 
h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_align i a = m
h_m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d' L✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_align i a = m

m': Meas

h_left: m' ∈ ms✝

h_right: Meas.adjust_align i m' = m

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i mlet ⟨
d': Doc
d', 
h_in: d' ∈ L✝
h_in, 
h_render: MeasRender F d' c c m'
h_render⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h': Resolve F d' c c (MeasureSet.set ms✝ h✝)
h' 
h_widen: Widen d' L✝
h_widen 
h_left: m' ∈ ms✝
h_left
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d'✝: Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d'✝ c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d'✝ L✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_align i a = m

m': Meas

h_left: m' ∈ ms✝

h_right: Meas.adjust_align i m' = m

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m'

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i mexists 
Doc.align: Doc → Doc
Doc.align 
d': Doc
d'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d'✝: Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d'✝ c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d'✝ L✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_align i a = m

m': Meas

h_left: m' ∈ ms✝

h_right: Meas.adjust_align i m' = m

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m'

Doc.align d' ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F (Doc.align d') c i m 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i msimp [*]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d'✝: Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d'✝ c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d'✝ L✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_align i a = m

m': Meas

h_left: m' ∈ ms✝

h_right: Meas.adjust_align i m' = m

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m'

MeasRender F (Doc.align d') c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i msubst 
h_right: Meas.adjust_align i m' = m
h_right
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d'✝ c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d'✝ L✝

m': Meas

h_left: m' ∈ ms✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m'

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_align i a = Meas.adjust_align i m'

MeasRender F (Doc.align d') c i (Meas.adjust_align i m') 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i mhave := 
MeasRender_doc: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas}, MeasRender F d c i m → Choiceless d → m.doc = d
MeasRender_doc 
h_render: MeasRender F d' c c m'
h_render (
Widen_choiceless: ∀ {d : Doc} {D : List Doc} {d_choiceless : Doc}, Widen d D → d_choiceless ∈ D → Choiceless d_choiceless
Widen_choiceless 
h_widen: Widen d'✝ L✝
h_widen 
h_in: d' ∈ L✝
h_in)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d'✝ c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d'✝ L✝

m': Meas

h_left: m' ∈ ms✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m'

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_align i a = Meas.adjust_align i m'

this: m'.doc = d'

MeasRender F (Doc.align d') c i (Meas.adjust_align i m')
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i msubst 
this: ?m.21975
this
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d' L✝

m': Meas

h_left: m' ∈ ms✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_align i a = Meas.adjust_align i m'

h_in: m'.doc ∈ L✝

h_render: MeasRender F m'.doc c c m'

MeasRender F (Doc.align m'.doc) c i (Meas.adjust_align i m') 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i mconstructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

L✝: List Doc

h_widen: Widen d' L✝

m': Meas

h_left: m' ∈ ms✝

h_m: ∃ a, a ∈ ms✝ ∧ Meas.adjust_align i a = Meas.adjust_align i m'

h_in: m'.doc ∈ L✝

h_render: MeasRender F m'.doc c c m'

h
MeasRender F m'.doc c c
  { last := (Meas.adjust_align i m').last, cost := (Meas.adjust_align i m').cost, doc := m'.doc,
    x := (Meas.adjust_align i m').x, y := m'.y }
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h: List.map (Meas.adjust_align i) ms✝ ≠ []

h_m: m ∈ List.map (Meas.adjust_align i) ms✝

L✝: List Doc

h_widen: Widen d' L✝

∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i msimpa [
Meas.adjust_align: {α : Type} → ℕ → Meas → Meas
Meas.adjust_align]
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_print: Resolve F (Doc.align d') c i (MeasureSet.set ms h)

h_widen: Widen (Doc.align d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase align_taint 
ms': MeasureSet
ms' _ _ => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
ms': MeasureSet
ms'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_bad✝: i > F.W

m✝: Meas

h✝: Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint (MeasureSet.tainted m✝))

tainted
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_bad✝: i > F.W

ms✝: List Meas

h✝¹: ms✝ ≠ []

h✝: Resolve F d' c c (MeasureSet.set ms✝ h✝¹)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint (MeasureSet.set ms✝ h✝¹))

set
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m<;>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_bad✝: i > F.W

m✝: Meas

h✝: Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint (MeasureSet.tainted m✝))

tainted
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

h_bad✝: i > F.W

ms✝: List Meas

h✝¹: ms✝ ≠ []

h✝: Resolve F d' c c (MeasureSet.set ms✝ h✝¹)

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint (MeasureSet.set ms✝ h✝¹))

set
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift, 
MeasureSet.taint: {α : Type} → MeasureSet → MeasureSet
MeasureSet.taint] at 
h_gen: MeasureSet.set ms h = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint (MeasureSet.tainted m✝))
h_gen
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.choice: Doc → Doc → Doc
Doc.choice 
d₁: Doc
d₁ 
d₂: Doc
d₂ =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.choice d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mgeneralize h_gen : 
MeasureSet.set: {α : Type} → (ms : List Meas) → ms ≠ [] → MeasureSet
MeasureSet.set 
_: List Meas
_ 
_: ?m.24257 ≠ []
_ = ms at 
h_print: Resolve F (Doc.choice d₁ d₂) c i (MeasureSet.set ms h)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms✝: List Meas

h: ms✝ ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms✝

d₁, d₂: Doc

h_widen: Widen (Doc.choice d₁ d₂) D

ms: MeasureSet

h_gen: MeasureSet.set ms✝ h = ms

h_print: Resolve F (Doc.choice d₁ d₂) c i ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.choice d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_widen: Widen (Doc.choice d₁ d₂) D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms✝: List Meas

h: ms✝ ≠ []

m: Meas

h_m: m ∈ ms✝

d₁, d₂: Doc

ms: MeasureSet

h_gen: MeasureSet.set ms✝ h = ms

h_print: Resolve F (Doc.choice d₁ d₂) c i ms

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

choice
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.choice d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase choice 
h_widen₁: Widen d₁ L₁✝
h_widen₁ 
h_widen₂: Widen d₂ L₂✝
h_widen₂ =>
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms✝: List Meas

h: ms✝ ≠ []

m: Meas

h_m: m ∈ ms✝

d₁, d₂: Doc

ms: MeasureSet

h_gen: MeasureSet.set ms✝ h = ms

h_print: Resolve F (Doc.choice d₁ d₂) c i ms

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F (Doc.choice d₁ d₂) c i ms
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝, ms'✝: MeasureSet

h_left✝: Resolve F d₁ c i ms✝

h_right✝: Resolve F d₂ c i ms'✝

h_gen: MeasureSet.set ms h = MeasureSet.union F ms✝ ms'✝

choice
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms✝: List Meas

h: ms✝ ≠ []

m: Meas

h_m: m ∈ ms✝

d₁, d₂: Doc

ms: MeasureSet

h_gen: MeasureSet.set ms✝ h = ms

h_print: Resolve F (Doc.choice d₁ d₂) c i ms

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase choice 
ms₁: MeasureSet
ms₁ 
ms₂: MeasureSet
ms₂ 
h₁: Resolve F d₁ c i ms₁
h₁ 
h₂: Resolve F d₂ c i ms₂
h₂ => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₁, ms₂: MeasureSet

h₁: Resolve F d₁ c i ms₁

h₂: Resolve F d₂ c i ms₂

h_gen: MeasureSet.set ms h = MeasureSet.union F ms₁ ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcases 
ms₁: MeasureSet
ms₁
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) ms₂

tainted
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂

set
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₁, ms₂: MeasureSet

h₁: Resolve F d₁ c i ms₁

h₂: Resolve F d₂ c i ms₂

h_gen: MeasureSet.set ms h = MeasureSet.union F ms₁ ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase tainted => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mdwi { 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcases 
ms₂: MeasureSet
ms₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝¹) (MeasureSet.tainted m✝)

tainted
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m }
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase set => 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union] at 
h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: ms = ms✝

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp at 
h_gen: ms = ms✝
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: ms = ms✝

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msubst 
h_gen: ms = ms✝
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

h✝: ms ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mlet ⟨
d_choiceless: Doc
d_choiceless, 
h: d_choiceless ∈ L₂✝ ∧ MeasRender F d_choiceless c i m
h⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h₂: Resolve F d₂ c i (MeasureSet.set ms h✝)
h₂ 
h_widen₂: Widen d₂ L₂✝
h_widen₂ 
h_m: m ∈ ms
h_m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h✝¹: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

h✝: ms ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms h✝)

d_choiceless: Doc

h: d_choiceless ∈ L₂✝ ∧ MeasRender F d_choiceless c i m

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mexists 
d_choiceless: Doc
d_choiceless
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h✝¹: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

h✝: ms ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms h✝)

d_choiceless: Doc

h: d_choiceless ∈ L₂✝ ∧ MeasRender F d_choiceless c i m

d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp [
h: d_choiceless ∈ L₂✝ ∧ MeasRender F d_choiceless c i m
h]
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₁, ms₂: MeasureSet

h₁: Resolve F d₁ c i ms₁

h₂: Resolve F d₂ c i ms₂

h_gen: MeasureSet.set ms h = MeasureSet.union F ms₁ ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase set 
ms': List Meas
ms' _ => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcases 
ms₂: MeasureSet
ms₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝) (MeasureSet.tainted m✝)

tainted
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝¹) (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase tainted => 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union] at 
h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝) (MeasureSet.tainted m✝)
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: ms = ms'

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp at 
h_gen: ms = ms'
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: ms = ms'

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msubst 
h_gen: ms = ms'
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h✝: ms ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mlet ⟨
d_choiceless: Doc
d_choiceless, 
h: d_choiceless ∈ L₁✝ ∧ MeasRender F d_choiceless c i m
h⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h₁: Resolve F d₁ c i (MeasureSet.set ms h✝)
h₁ 
h_widen₁: Widen d₁ L₁✝
h_widen₁ 
h_m: m ∈ ms
h_m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h✝¹: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h✝: ms ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms h✝)

d_choiceless: Doc

h: d_choiceless ∈ L₁✝ ∧ MeasRender F d_choiceless c i m

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mexists 
d_choiceless: Doc
d_choiceless
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h✝¹: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h✝: ms ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms h✝)

d_choiceless: Doc

h: d_choiceless ∈ L₁✝ ∧ MeasRender F d_choiceless c i m

d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp [
h: d_choiceless ∈ L₁✝ ∧ MeasRender F d_choiceless c i m
h]
Goals accomplished! 🐙
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase set 
ms'': List Meas
ms'' _ => 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝¹) (MeasureSet.set ms'' h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union] at 
h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝¹) (MeasureSet.set ms'' h✝)
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h_gen: ms = merge F (ms', ms'')

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝¹) (MeasureSet.set ms'' h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msubst 
h_gen: ms = merge F (ms', ms'')
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ merge F (ms', ms'')

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝¹) (MeasureSet.set ms'' h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mreplace 
h_m: ?m.44675
h_m := 
merge_pareto_subset: ∀ {α : Type} {m : Meas} {F : Factory α} {ms₁ ms₂ : List Meas},
  m ∈ merge F (ms₁, ms₂) → pareto F ms₁ → pareto F ms₂ → m ∈ ms₁ ∨ m ∈ ms₂
merge_pareto_subset 
h_m: m ∈ merge F (ms', ms'')
h_m (
Resolve_pareto: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h_non_empty : ms ≠ []},
  Resolve F d c i (MeasureSet.set ms h_non_empty) → pareto F ms
Resolve_pareto 
h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)
h₁) (
Resolve_pareto: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h_non_empty : ms ≠ []},
  Resolve F d c i (MeasureSet.set ms h_non_empty) → pareto F ms
Resolve_pareto 
h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)
h₂)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ ms' ∨ m ∈ ms''

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝¹) (MeasureSet.set ms'' h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcases 
h_m: ?m.44675
h_m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝²: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝²)

ms'': List Meas

h✝¹: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝¹)

h: merge F (ms', ms'') ≠ []

h✝: m ∈ ms'

inl
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝²: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝²)

ms'': List Meas

h✝¹: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝¹)

h: merge F (ms', ms'') ≠ []

h✝: m ∈ ms''

inr
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝¹) (MeasureSet.set ms'' h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase inl 
h_m: ?m.44726
h_m => 
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ ms'

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mlet ⟨
d_choiceless: Doc
d_choiceless, _⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)
h₁ 
h_widen₁: Widen d₁ L₁✝
h_widen₁ 
h_m: ?m.44726
h_m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝²: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝²)

ms'': List Meas

h✝¹: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝¹)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ ms'

d_choiceless: Doc

h✝: d_choiceless ∈ L₁✝ ∧ MeasRender F d_choiceless c i m

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ ms'

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mexists 
d_choiceless: Doc
d_choiceless
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝²: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝²)

ms'': List Meas

h✝¹: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝¹)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ ms'

d_choiceless: Doc

h✝: d_choiceless ∈ L₁✝ ∧ MeasRender F d_choiceless c i m

d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ ms'

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp [*]
Goals accomplished! 🐙
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h_gen: MeasureSet.set ms h = MeasureSet.union F (MeasureSet.set ms' h✝¹) (MeasureSet.set ms'' h✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase inr 
h_m: ?m.44727
h_m => 
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ ms''

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mlet ⟨
d_choiceless: Doc
d_choiceless, _⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)
h₂ 
h_widen₂: Widen d₂ L₂✝
h_widen₂ 
h_m: ?m.44727
h_m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝²: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝²)

ms'': List Meas

h✝¹: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝¹)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ ms''

d_choiceless: Doc

h✝: d_choiceless ∈ L₂✝ ∧ MeasRender F d_choiceless c i m

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ ms''

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mexists 
d_choiceless: Doc
d_choiceless
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝²: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝²)

ms'': List Meas

h✝¹: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝¹)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ ms''

d_choiceless: Doc

h✝: d_choiceless ∈ L₂✝ ∧ MeasRender F d_choiceless c i m

d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms'': List Meas

h✝: ms'' ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms'' h✝)

h: merge F (ms', ms'') ≠ []

h_m: m ∈ ms''

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp [*]
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d₁: Doc
d₁ 
d₂: Doc
d₂ =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.concat d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_print: Resolve F d c i (MeasureSet.set ms h)

h_widen: Widen d D

h_m: m ∈ ms

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_widen: Widen (Doc.concat d₁ d₂) D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.set ms h)

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

concat
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i m
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.concat d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.set ms h)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i m
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

D: List Doc

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.set ms h)

h_widen: Widen (Doc.concat d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mapply 
ResolveConcat_valid: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d₂ : Doc} {i : ℕ} {ms_r : List Meas} {h_non_empty_r : ms_r ≠ []}
  {d₁ : Doc} {L₁ L₂ : List Doc} {c : ℕ} {orig_ms : List Meas} {h_non_empty : orig_ms ≠ []} (m : Meas),
  ResolveConcat F ms d₂ i (MeasureSet.set ms_r h_non_empty_r) →
    Widen d₁ L₁ →
      Widen d₂ L₂ →
        Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty) →
          (∀ (x : Meas), x ∈ ms → x ∈ orig_ms) →
            m ∈ ms_r →
              ∃ d_choiceless,
                d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧                   MeasRender F d_choiceless c i m
ResolveConcat_valid
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_right
ResolveConcat F ?concat.concat_set.ms ?concat.concat_set.d₂ i
  (MeasureSet.set ?concat.concat_set.ms_r ?concat.concat_set.h_non_empty_r)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_widen₁
Widen ?concat.concat_set.d₁ L₁✝
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_widen₂
Widen ?concat.concat_set.d₂ L₂✝
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_left
Resolve F ?concat.concat_set.d₁ c i (MeasureSet.set ?concat.concat_set.orig_ms ?concat.concat_set.h_non_empty)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_transfer
∀ (x : Meas), x ∈ ?concat.concat_set.ms → x ∈ ?concat.concat_set.orig_ms
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_m
m ∈ ?concat.concat_set.ms_r
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.ms
List Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.d₂
Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.ms_r
List Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_non_empty_r
?concat.concat_set.ms_r ≠ []
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.d₁
Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.orig_ms
List Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_non_empty
?concat.concat_set.orig_ms ≠ [] 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i m<;>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_right
ResolveConcat F ?concat.concat_set.ms ?concat.concat_set.d₂ i
  (MeasureSet.set ?concat.concat_set.ms_r ?concat.concat_set.h_non_empty_r)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_widen₁
Widen ?concat.concat_set.d₁ L₁✝
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_widen₂
Widen ?concat.concat_set.d₂ L₂✝
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_left
Resolve F ?concat.concat_set.d₁ c i (MeasureSet.set ?concat.concat_set.orig_ms ?concat.concat_set.h_non_empty)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_transfer
∀ (x : Meas), x ∈ ?concat.concat_set.ms → x ∈ ?concat.concat_set.orig_ms
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_m
m ∈ ?concat.concat_set.ms_r
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.ms
List Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.d₂
Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.ms_r
List Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_non_empty_r
?concat.concat_set.ms_r ≠ []
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.d₁
Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.orig_ms
List Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_non_empty
?concat.concat_set.orig_ms ≠ [] 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i mfirst | 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_m
m ∈ msassumption
Goals accomplished! 🐙 | 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ms: List Meas

h: ms ≠ []

m: Meas

h_m: m ∈ ms

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h)

concat.concat_set.h_m
m ∈ mssimp
Goals accomplished! 🐙   

  theorem 
ResolveConcat_valid: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d₂ : Doc} {i : ℕ} {ms_r : List Meas} {h_non_empty_r : ms_r ≠ []}
  {d₁ : Doc} {L₁ L₂ : List Doc} {c : ℕ} {orig_ms : List Meas} {h_non_empty : orig_ms ≠ []} (m : Meas),
  ResolveConcat F ms d₂ i (MeasureSet.set ms_r h_non_empty_r) →
    Widen d₁ L₁ →
      Widen d₂ L₂ →
        Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty) →
          (∀ (x : Meas), x ∈ ms → x ∈ orig_ms) →
            m ∈ ms_r →
              ∃ d_choiceless,
                d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧                   MeasRender F d_choiceless c i m
ResolveConcat_valid 
      (
m: Meas
m : 
Meas: {α : Type} → Type
Meas)
      (
h_right: ResolveConcat F ms d₂ i (MeasureSet.set ms_r h_non_empty_r)
h_right : 
ResolveConcat: {α : Type} → Factory α → List Meas → Doc → ℕ → MeasureSet → Prop
ResolveConcat 
F: ?m.150
F 
ms: ?m.160
ms 
d₂: ?m.170
d₂ 
i: ?m.179
i (
MeasureSet.set: {α : Type} → (ms : List Meas) → ms ≠ [] → MeasureSet
MeasureSet.set 
ms_r: ?m.191
ms_r 
h_non_empty_r: ?m.202
h_non_empty_r)) 
      (
h_widen₁: Widen d₁ L₁
h_widen₁ : 
Widen: Doc → List Doc → Prop
Widen 
d₁: ?m.218
d₁ 
L₁: ?m.231
L₁) (
h_widen₂: Widen d₂ L₂
h_widen₂ : 
Widen: Doc → List Doc → Prop
Widen 
d₂: ?m.170
d₂ 
L₂: ?m.246
L₂)
      (
h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)
h_left : 
Resolve: {α : Type} → Factory α → Doc → ℕ → ℕ → MeasureSet → Prop
Resolve 
F: ?m.150
F 
d₁: ?m.218
d₁ 
c: ?m.264
c 
i: ?m.179
i (
MeasureSet.set: {α : Type} → (ms : List Meas) → ms ≠ [] → MeasureSet
MeasureSet.set 
orig_ms: ?m.284
orig_ms 
h_non_empty: ?m.304
h_non_empty))
      (
h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms
h_transfer : ∀ 
x: ?m.326
x, 
x: ?m.326
x ∈ 
ms: ?m.160
ms → 
x: ?m.326
x ∈ 
orig_ms: ?m.284
orig_ms)
      (
h_m: m ∈ ms_r
h_m : 
m: Meas
m ∈ 
ms_r: ?m.191
ms_r) :
      ∃ 
d_choiceless: ?m.407
d_choiceless,
        
d_choiceless: ?m.407
d_choiceless ∈ 
List.join: {α : Type ?u.414} → List (List α) → List α
List.join (
List.map: {α : Type ?u.417} → {β : Type ?u.416} → (α → β) → List α → List β
List.map (fun 
d₁: ?m.422
d₁ => 
List.map: {α : Type ?u.425} → {β : Type ?u.424} → (α → β) → List α → List β
List.map (fun 
d₂: ?m.430
d₂ => 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d₁: ?m.422
d₁ 
d₂: ?m.430
d₂) 
L₂: ?m.246
L₂) 
L₁: ?m.231
L₁) ∧ 
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: ?m.150
F  
d_choiceless: ?m.407
d_choiceless 
c: ?m.264
c 
i: ?m.179
i 
m: Meas
m := by
Goals accomplished! 🐙 
    
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_right: ResolveConcat F ms d₂ i (MeasureSet.set ms_r h_non_empty_r)

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

h_m: m ∈ ms_r

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mgeneralize h_ml : 
MeasureSet.set: {α : Type} → (ms : List Meas) → ms ≠ [] → MeasureSet
MeasureSet.set 
_: List Meas
_ 
_: ?m.58542 ≠ []
_ = ml at 
h_right: ResolveConcat F ms d₂ i (MeasureSet.set ms_r h_non_empty_r)
h_right
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

h_right: ResolveConcat F ms d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
    
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_right: ResolveConcat F ms d₂ i (MeasureSet.set ms_r h_non_empty_r)

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

h_m: m ∈ ms_r

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mmatch 
ms: List Meas
ms with
    
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

h_right: ResolveConcat F ms d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m| [] =>
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

h_transfer: ∀ (x : Meas), x ∈ [] → x ∈ orig_ms

h_right: ResolveConcat F [] d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

h_right: ResolveConcat F ms d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcontradiction
Goals accomplished! 🐙 
    
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

h_right: ResolveConcat F ms d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m| [
m₀: Meas
m₀] =>
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

h_right: ResolveConcat F [m₀] d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

h_right: ResolveConcat F ms d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
h_right: ResolveConcat F [m₀] d₂ i ml
h_right
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

h_current✝: ResolveConcatOne F d₂ m₀ i ml

one
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

msr✝, msr'✝: MeasureSet

h_current✝: ResolveConcatOne F d₂ m₀ i msr'✝

h_rest✝: ResolveConcat F [] d₂ i msr✝

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr'✝ msr✝

cons
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
      
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

h_right: ResolveConcat F [m₀] d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase cons => 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

msr✝, msr'✝: MeasureSet

h_current✝: ResolveConcatOne F d₂ m₀ i msr'✝

h_rest✝: ResolveConcat F [] d₂ i msr✝

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr'✝ msr✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcontradiction
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

h_right: ResolveConcat F [m₀] d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase one 
h_current: ResolveConcatOne F d₂ m₀ i ml
h_current =>
        
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m₀ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
h_current: ResolveConcatOne F d₂ m₀ i ml
h_current
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

m'✝: Meas

h✝: Resolve F d₂ m₀.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.tainted (Meas.concat F m₀ m'✝)

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h✝: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
        
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m₀ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase tainted => 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

m'✝: Meas

h✝: Resolve F d₂ m₀.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.tainted (Meas.concat F m₀ m'✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcontradiction
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m₀ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase set 
h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)
h_right => 
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])
h_ml
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝)

refl
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mreplace 
h_m: ?m.67119
h_m := 
dedup_member: ∀ {α : Type} {m : Meas} {F : Factory α} {ms : List Meas}, m ∈ dedup F ms → m ∈ ms
dedup_member 
h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝)
h_m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: m ∈ List.map (fun m' => Meas.concat F m₀ m') ms✝

refl
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp at 
h_m: ?m.67119
h_m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

refl
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
m_right: Meas
m_right, ⟨
h_in_right: m_right ∈ ms✝
h_in_right, _⟩⟩ := 
h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m
h_m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝: Meas.concat F m₀ m_right = m

refl
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mhave 
h_in_left: m₀ ∈ orig_ms
h_in_left : 
m₀: Meas
m₀ ∈ 
orig_ms: List Meas
orig_ms := 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝: Meas.concat F m₀ m_right = m

refl
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mby
Goals accomplished! 🐙
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝: Meas.concat F m₀ m_right = m

m₀ ∈ orig_msapply 
h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms
h_transfer
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝: Meas.concat F m₀ m_right = m

a
m₀ ∈ [m₀] 
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝: Meas.concat F m₀ m_right = m

m₀ ∈ orig_msapply 
List.mem_singleton_self: ∀ {α : Type ?u.68272} (a : α), a ∈ [a]
List.mem_singleton_self 
m₀: Meas
m₀
Goals accomplished! 🐙
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mobtain 
⟨d_choiceless_left, ⟨_, _⟩⟩: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₀
⟨
d_choiceless_left: Doc
d_choiceless_left
⟨d_choiceless_left, ⟨_, _⟩⟩: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₀
, 
⟨_, _⟩: d_choiceless_left ∈ L₁ ∧ MeasRender F d_choiceless_left c i m₀
⟨
_: d_choiceless_left ∈ L₁
_
⟨_, _⟩: d_choiceless_left ∈ L₁ ∧ MeasRender F d_choiceless_left c i m₀
, 
_: MeasRender F d_choiceless_left c i m₀
_
⟨_, _⟩: d_choiceless_left ∈ L₁ ∧ MeasRender F d_choiceless_left c i m₀
⟩
⟨d_choiceless_left, ⟨_, _⟩⟩: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₀
⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)
h_left 
h_widen₁: Widen d₁ L₁
h_widen₁ 
h_in_left: m₀ ∈ orig_ms
h_in_left
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝¹: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝: d_choiceless_left ∈ L₁

right✝: MeasRender F d_choiceless_left c i m₀

refl.intro.intro
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
d_choiceless_right: Doc
d_choiceless_right, ⟨_, _⟩⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)
h_right 
h_widen₂: Widen d₂ L₂
h_widen₂ 
h_in_right: m_right ∈ ms✝
h_in_right
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

refl.intro.intro
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 

          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mexists 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d_choiceless_left: Doc
d_choiceless_left 
d_choiceless_right: Doc
d_choiceless_right
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

refl.intro.intro
Doc.concat d_choiceless_left d_choiceless_right ∈     List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧   MeasRender F (Doc.concat d_choiceless_left d_choiceless_right) c i m 
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp [*]
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

refl.intro.intro
MeasRender F (Doc.concat d_choiceless_left d_choiceless_right) c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mconstructor
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

refl.intro.intro.h₁
MeasRender F d_choiceless_left c i ?refl.intro.intro.m₁
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

refl.intro.intro.h₂
MeasRender F d_choiceless_right ?refl.intro.intro.m₁.last i ?refl.intro.intro.m₂
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

refl.intro.intro.h
m = Meas.concat F ?refl.intro.intro.m₁ ?refl.intro.intro.m₂
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

refl.intro.intro.m₁
Meas
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

refl.intro.intro.m₂
Meas
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase h₁ | h₂ => 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

MeasRender F d_choiceless_left c i ?refl.intro.intro.m₁assumption
Goals accomplished! 🐙
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.set ms_r h_non_empty_r =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase h => 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

m = Meas.concat F m₀ m_rightsymm
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

Meas.concat F m₀ m_right = m;
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

Meas.concat F m₀ m_right = m 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₀: Meas

h_transfer: ∀ (x : Meas), x ∈ [m₀] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_right: Resolve F d₂ m₀.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₀ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₀ a = m

m_right: Meas

h_in_right: m_right ∈ ms✝

right✝²: Meas.concat F m₀ m_right = m

h_in_left: m₀ ∈ orig_ms

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₀

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₀.last i m_right

m = Meas.concat F m₀ m_rightassumption
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

h_right: ResolveConcat F ms d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m| 
m₁: Meas
m₁ :: 
m₂: Meas
m₂ :: 
tl: List Meas
tl =>
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

h_right: ResolveConcat F (m₁ :: m₂ :: tl) d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

h_right: ResolveConcat F ms d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
h_right: ResolveConcat F (m₁ :: m₂ :: tl) d₂ i ml
h_right
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr✝, msr'✝: MeasureSet

h_current✝: ResolveConcatOne F d₂ m₁ i msr'✝

h_rest✝: ResolveConcat F (m₂ :: tl) d₂ i msr✝

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr'✝ msr✝

cons
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
      
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

ml: MeasureSet

h_ml: MeasureSet.set ms_r h_non_empty_r = ml

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

h_right: ResolveConcat F (m₁ :: m₂ :: tl) d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase cons 
msr: MeasureSet
msr 
msr': MeasureSet
msr' 
h_current: ResolveConcatOne F d₂ m₁ i msr'
h_current 
h_rest: ResolveConcat F (m₂ :: tl) d₂ i msr
h_rest => 
      
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr, msr': MeasureSet

h_current: ResolveConcatOne F d₂ m₁ i msr'

h_rest: ResolveConcat F (m₂ :: tl) d₂ i msr

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr' msr

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
msr: MeasureSet
msr
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr': MeasureSet

h_current: ResolveConcatOne F d₂ m₁ i msr'

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr' (MeasureSet.tainted m✝)

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr': MeasureSet

h_current: ResolveConcatOne F d₂ m₁ i msr'

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr' (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr, msr': MeasureSet

h_current: ResolveConcatOne F d₂ m₁ i msr'

h_rest: ResolveConcat F (m₂ :: tl) d₂ i msr

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr' msr

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase tainted => 
        
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr': MeasureSet

h_current: ResolveConcatOne F d₂ m₁ i msr'

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr' (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
msr': MeasureSet
msr'
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝¹: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝¹)

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.tainted m✝¹)

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝)

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
        
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr': MeasureSet

h_current: ResolveConcatOne F d₂ m₁ i msr'

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr' (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase tainted => 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝¹: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝¹)

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.tainted m✝¹)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcontradiction
Goals accomplished! 🐙 
        
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr': MeasureSet

h_current: ResolveConcatOne F d₂ m₁ i msr'

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr' (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase set => 
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union] at 
h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝)
h_ml
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: ms_r = ms✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msubst 
h_ml: ms_r = ms✝
h_ml
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms_r h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms_r h✝)
h_current
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h✝¹: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty✝)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase set 
h_non_empty: ms✝ ≠ []
h_non_empty 
h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)
h_current _ => 
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mreplace 
h_m: ?m.86087
h_m := 
dedup_member: ∀ {α : Type} {m : Meas} {F : Factory α} {ms : List Meas}, m ∈ dedup F ms → m ∈ ms
dedup_member 
h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)
h_m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ List.map (fun m' => Meas.concat F m₁ m') ms✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp at 
h_m: ?m.86087
h_m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
m_right: Meas
m_right, ⟨
h_in: m_right ∈ ms✝
h_in, _⟩⟩ := 
h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m
h_m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝: Meas.concat F m₁ m_right = m

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mhave := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)
h_left 
h_widen₁: Widen d₁ L₁
h_widen₁ (
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝: Meas.concat F m₁ m_right = m

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝: Meas.concat F m₁ m_right = m

?m.87122 ∈ orig_ms{
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝: Meas.concat F m₁ m_right = m

?m.87122 ∈ orig_ms 
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝: Meas.concat F m₁ m_right = m

?m.87122 ∈ orig_msapply 
h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms
h_transfer
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝: Meas.concat F m₁ m_right = m

a
?m.87122 ∈ m₁ :: m₂ :: tl
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝: Meas.concat F m₁ m_right = m

?m.87122 ∈ orig_msapply 
List.mem_cons_self: ∀ {α : Type ?u.87131} (a : α) (l : List α), a ∈ a :: l
List.mem_cons_self
Goals accomplished! 🐙
            }
Goals accomplished! 🐙)
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
d_choiceless_left: Doc
d_choiceless_left, ⟨_, _⟩⟩ := 
this: ?m.87113
this
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝¹: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝: d_choiceless_left ∈ L₁

right✝: MeasRender F d_choiceless_left c i m₁

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
d_choiceless_right: Doc
d_choiceless_right, ⟨_, _⟩⟩ := @
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
_: Type
_ 
F: Factory α✝
F 
d₂: Doc
d₂ 
m₁: Meas
m₁.
last: {α : Type} → Meas → ℕ
last 
i: ℕ
i 
_: List Meas
_ 
h_non_empty: ms✝ ≠ []
h_non_empty 
_: List Doc
_ 
m_right: Meas
m_right 
h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)
h_current 
h_widen₂: Widen d₂ L₂
h_widen₂ 
h_in: m_right ∈ ms✝
h_in
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mexists 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d_choiceless_left: Doc
d_choiceless_left 
d_choiceless_right: Doc
d_choiceless_right
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

Doc.concat d_choiceless_left d_choiceless_right ∈     List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧   MeasRender F (Doc.concat d_choiceless_left d_choiceless_right) c i m 
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp [*]
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

MeasRender F (Doc.concat d_choiceless_left d_choiceless_right) c i m
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mconstructor
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

h₁
MeasRender F d_choiceless_left c i ?m₁
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

h₂
MeasRender F d_choiceless_right ?m₁.last i ?m₂
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

h
m = Meas.concat F ?m₁ ?m₂
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

m₁
Meas
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

m₂
Meas
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase h₁ | h₂ => 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

MeasRender F d_choiceless_right m₁.last i ?m₂assumption
Goals accomplished! 🐙
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase h => 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

m = Meas.concat F m₁ m_rightsymm
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

Meas.concat F m₁ m_right = m;
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

Meas.concat F m₁ m_right = m 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h_non_empty_r, h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_m: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

m_right: Meas

h_in: m_right ∈ ms✝

right✝²: Meas.concat F m₁ m_right = m

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i m_right

m = Meas.concat F m₁ m_rightassumption
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr, msr': MeasureSet

h_current: ResolveConcatOne F d₂ m₁ i msr'

h_rest: ResolveConcat F (m₂ :: tl) d₂ i msr

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr' msr

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase set => 
        
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr': MeasureSet

h_current: ResolveConcatOne F d₂ m₁ i msr'

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr' (MeasureSet.set ms✝ h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
msr': MeasureSet
msr'
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝ h✝)

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms✝¹ h✝¹)

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
        
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr': MeasureSet

h_current: ResolveConcatOne F d₂ m₁ i msr'

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr' (MeasureSet.set ms✝ h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase tainted => 
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝ h✝)

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union] at 
h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)
h_ml
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝ h✝)

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h_ml: ms_r = ms✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝ h✝)

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msubst 
h_ml: ms_r = ms✝
h_ml
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝ h✝)

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
d_choiceless: Doc
d_choiceless, _⟩ := 
ResolveConcat_valid: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d₂ : Doc} {i : ℕ} {ms_r : List Meas} {h_non_empty_r : ms_r ≠ []}
  {d₁ : Doc} {L₁ L₂ : List Doc} {c : ℕ} {orig_ms : List Meas} {h_non_empty : orig_ms ≠ []} (m : Meas),
  ResolveConcat F ms d₂ i (MeasureSet.set ms_r h_non_empty_r) →
    Widen d₁ L₁ →
      Widen d₂ L₂ →
        Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty) →
          (∀ (x : Meas), x ∈ ms → x ∈ orig_ms) →
            m ∈ ms_r →
              ∃ d_choiceless,
                d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧                   MeasRender F d_choiceless c i m
ResolveConcat_valid 
m: Meas
m 
h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)
h_rest 
h_widen₁: Widen d₁ L₁
h_widen₁ 
h_widen₂: Widen d₂ L₂
h_widen₂ 
h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)
h_left (
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_ms{
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_ms
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_msintro 
_: Meas
_ 
_: x✝ ∈ m₂ :: tl
_
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)

x✝: Meas

a✝: x✝ ∈ m₂ :: tl

x✝ ∈ orig_ms
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_msapply 
h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms
h_transfer
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)

x✝: Meas

a✝: x✝ ∈ m₂ :: tl

a
x✝ ∈ m₁ :: m₂ :: tl 
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_msapply 
List.Mem.tail: ∀ {α : Type ?u.102018} {a : α} (b : α) {as : List α}, List.Mem a as → List.Mem a (b :: as)
List.Mem.tail
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)

x✝: Meas

a✝: x✝ ∈ m₂ :: tl

a.a
List.Mem x✝ (m₂ :: tl)
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝)

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_msassumption
Goals accomplished! 🐙
            }
Goals accomplished! 🐙) 
h_m: m ∈ ms_r
h_m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h✝¹: ms_r ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms_r h✝¹)

d_choiceless: Doc

h✝: d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧   MeasRender F d_choiceless c i m

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝ h✝)

m✝: Meas

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mexists 
d_choiceless: Doc
d_choiceless
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

msr': MeasureSet

h_current: ResolveConcatOne F d₂ m₁ i msr'

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F msr' (MeasureSet.set ms✝ h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase set => 
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms✝¹ h✝¹)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union] at 
h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms✝¹ h✝¹)
h_ml
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: ms_r = merge F (ms✝, ms✝¹)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms✝¹ h✝¹)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msubst 
h_ml: ms_r = merge F (ms✝, ms✝¹)
h_ml
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms✝¹ h✝¹)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
merge_pareto_subset: ∀ {α : Type} {m : Meas} {F : Factory α} {ms₁ ms₂ : List Meas},
  m ∈ merge F (ms₁, ms₂) → pareto F ms₁ → pareto F ms₂ → m ∈ ms₁ ∨ m ∈ ms₂
merge_pareto_subset 
h_m: m ∈ merge F (ms✝, ms✝¹)
h_m 
            (
ResolveConcatOne_pareto: ∀ {α : Type} {F : Factory α} {d : Doc} {m : Meas} {i : ℕ} {msr : List Meas} {h_non_empty : msr ≠ []},
  ResolveConcatOne F d m i (MeasureSet.set msr h_non_empty) → pareto F msr
ResolveConcatOne_pareto 
h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)
h_current)
            (
ResolveConcat_pareto: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d : Doc} {i : ℕ} {msr : List Meas} {h_non_empty : msr ≠ []},
  ResolveConcat F ms d i (MeasureSet.set msr h_non_empty) → pareto F msr
ResolveConcat_pareto 
h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)
h_rest)
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝²: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝²)

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝¹)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h✝: m ∈ ms✝

inl
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝²: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝²)

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝¹)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h✝: m ∈ ms✝¹

inr
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms✝¹ h✝¹)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase inl 
h_d: ?m.108668
h_d => 
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)
h_current
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝²: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝²)

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h✝¹: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty✝)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase set 
h_non_empty: ms✝ ≠ []
h_non_empty 
h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)
h_current _ => 
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mhave := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)
h_left 
h_widen₁: Widen d₁ L₁
h_widen₁ (
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

?m.108998 ∈ orig_ms{
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

?m.108998 ∈ orig_ms 
                
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

?m.108998 ∈ orig_msapply 
h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms
h_transfer
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

a
?m.108998 ∈ m₁ :: m₂ :: tl
                
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

?m.108998 ∈ orig_msapply 
List.mem_cons_self: ∀ {α : Type ?u.109007} (a : α) (l : List α), a ∈ a :: l
List.mem_cons_self
Goals accomplished! 🐙
              }
Goals accomplished! 🐙)
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
d_choiceless_left: Doc
d_choiceless_left, ⟨_, _⟩⟩ := 
this: ?m.108989
this
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝: d_choiceless_left ∈ L₁

right✝: MeasRender F d_choiceless_left c i m₁

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mreplace 
h_d: ?m.109152
h_d := 
dedup_member: ∀ {α : Type} {m : Meas} {F : Factory α} {ms : List Meas}, m ∈ dedup F ms → m ∈ ms
dedup_member 
h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)
h_d
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝: d_choiceless_left ∈ L₁

right✝: MeasRender F d_choiceless_left c i m₁

h_d: m ∈ List.map (fun m' => Meas.concat F m₁ m') ms✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp at 
h_d: ?m.109152
h_d
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝: d_choiceless_left ∈ L₁

right✝: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
_: Meas
_, ⟨
h_star: w✝ ∈ ms✝
h_star, _⟩⟩ := 
h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m
h_d
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝: d_choiceless_left ∈ L₁

right✝¹: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝: Meas.concat F m₁ w✝ = m

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
d_choiceless_right: Doc
d_choiceless_right, ⟨_, _⟩⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)
h_current 
h_widen₂: Widen d₂ L₂
h_widen₂ 
h_star: w✝ ∈ ms✝
h_star
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mexists 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d_choiceless_left: Doc
d_choiceless_left 
d_choiceless_right: Doc
d_choiceless_right
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

Doc.concat d_choiceless_left d_choiceless_right ∈     List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧   MeasRender F (Doc.concat d_choiceless_left d_choiceless_right) c i m 
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp [*]
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

MeasRender F (Doc.concat d_choiceless_left d_choiceless_right) c i m
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mconstructor
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

h₁
MeasRender F d_choiceless_left c i ?m₁
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

h₂
MeasRender F d_choiceless_right ?m₁.last i ?m₂
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

h
m = Meas.concat F ?m₁ ?m₂
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

m₁
Meas
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

m₂
Meas
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase h₁ | h₂ => 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

MeasRender F d_choiceless_right m₁.last i ?m₂assumption
Goals accomplished! 🐙
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

h_d: m ∈ dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase h => 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

m = Meas.concat F m₁ w✝symm
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

Meas.concat F m₁ w✝ = m;
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

Meas.concat F m₁ w✝ = m 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty✝: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty✝)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h_non_empty: ms✝ ≠ []

h_current: Resolve F d₂ m₁.last i (MeasureSet.set ms✝ h_non_empty)

h✝: dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝) ≠ []

h_non_empty_r: merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹) ≠ []

h_m: m ∈ merge F (dedup F (List.map (fun m' => Meas.concat F m₁ m') ms✝), ms✝¹)

this: ∃ d_choiceless, d_choiceless ∈ L₁ ∧ MeasRender F d_choiceless c i m₁

d_choiceless_left: Doc

left✝¹: d_choiceless_left ∈ L₁

right✝²: MeasRender F d_choiceless_left c i m₁

h_d: ∃ a, a ∈ ms✝ ∧ Meas.concat F m₁ a = m

w✝: Meas

h_star: w✝ ∈ ms✝

right✝¹: Meas.concat F m₁ w✝ = m

d_choiceless_right: Doc

left✝: d_choiceless_right ∈ L₂

right✝: MeasRender F d_choiceless_right m₁.last i w✝

m = Meas.concat F m₁ w✝assumption
Goals accomplished! 🐙
          
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ms_r: List Meas

h_non_empty_r: ms_r ≠ []

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_m: m ∈ ms_r

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.set ms_r h_non_empty_r = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms✝¹ h✝¹)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase inr 
h_d: ?m.108669
h_d => 
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
d_choiceless: Doc
d_choiceless, _⟩ := 
ResolveConcat_valid: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d₂ : Doc} {i : ℕ} {ms_r : List Meas} {h_non_empty_r : ms_r ≠ []}
  {d₁ : Doc} {L₁ L₂ : List Doc} {c : ℕ} {orig_ms : List Meas} {h_non_empty : orig_ms ≠ []} (m : Meas),
  ResolveConcat F ms d₂ i (MeasureSet.set ms_r h_non_empty_r) →
    Widen d₁ L₁ →
      Widen d₂ L₂ →
        Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty) →
          (∀ (x : Meas), x ∈ ms → x ∈ orig_ms) →
            m ∈ ms_r →
              ∃ d_choiceless,
                d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧                   MeasRender F d_choiceless c i m
ResolveConcat_valid 
m: Meas
m 
h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)
h_rest 
h_widen₁: Widen d₁ L₁
h_widen₁ 
h_widen₂: Widen d₂ L₂
h_widen₂ 
h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)
h_left (
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_ms{
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_ms
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_msintro 
_: Meas
_ 
_: x✝ ∈ m₂ :: tl
_
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

x✝: Meas

a✝: x✝ ∈ m₂ :: tl

x✝ ∈ orig_ms
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_msapply 
h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms
h_transfer
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

x✝: Meas

a✝: x✝ ∈ m₂ :: tl

a
x✝ ∈ m₁ :: m₂ :: tl 
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_msapply 
List.Mem.tail: ∀ {α : Type ?u.125121} {a : α} (b : α) {as : List α}, List.Mem a as → List.Mem a (b :: as)
List.Mem.tail
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

x✝: Meas

a✝: x✝ ∈ m₂ :: tl

a.a
List.Mem x✝ (m₂ :: tl)
              
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

∀ (x : Meas), x ∈ m₂ :: tl → x ∈ orig_msassumption
Goals accomplished! 🐙
            }
Goals accomplished! 🐙) 
h_d: ?m.108669
h_d
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝²: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝²)

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝¹)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

d_choiceless: Doc

h✝: d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧   MeasRender F d_choiceless c i m

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

m: Meas

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m₁, m₂: Meas

tl: List Meas

h_transfer: ∀ (x : Meas), x ∈ m₁ :: m₂ :: tl → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F (m₂ :: tl) d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m₁ i (MeasureSet.set ms✝ h✝)

h_non_empty_r: merge F (ms✝, ms✝¹) ≠ []

h_m: m ∈ merge F (ms✝, ms✝¹)

h_d: m ∈ ms✝¹

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mexists 
d_choiceless: Doc
d_choiceless
Goals accomplished! 🐙   
end
termination_by 
  ResolveConcat_valid => (
d₁: Doc
d₁.
size: Doc → ℕ
size + 
d₂: Doc
d₂.
size: Doc → ℕ
size + 
1: ?m.145095
1, 
0: ?m.145173
0, 
ms: List Meas
ms.
length: {α : Type ?u.145183} → List α → ℕ
length)
  Resolve_valid => (
d: Doc
d.
size: Doc → ℕ
size, 
1: ?m.144652
1, 
0: ?m.144663
0)

mutual 
  /--
  The validity theorem for tainted result (the second part of Theorem 5.8)
  -/
  theorem 
Resolve_tainted_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas} {D : List Doc},
  Resolve F d c i (MeasureSet.tainted m) →
    Widen d D → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_tainted_valid (
h_print: Resolve F d c i (MeasureSet.tainted m)
h_print : 
Resolve: {α : Type} → Factory α → Doc → ℕ → ℕ → MeasureSet → Prop
Resolve 
F: ?m.410385
F 
d: ?m.410392
d 
c: ?m.410398
c 
i: ?m.410404
i (
MeasureSet.tainted: {α : Type} → Meas → MeasureSet
MeasureSet.tainted 
m: ?m.410413
m))
      (
h_widen: Widen d D
h_widen : 
Widen: Doc → List Doc → Prop
Widen 
d: ?m.410392
d 
D: ?m.410424
D) : ∃ 
d_choiceless: ?m.410438
d_choiceless, 
d_choiceless: ?m.410438
d_choiceless ∈ 
D: ?m.410424
D ∧ 
      
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: ?m.410385
F 
d_choiceless: ?m.410438
d_choiceless 
c: ?m.410398
c 
i: ?m.410404
i 
m: ?m.410413
m := by
Goals accomplished! 🐙 
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mmatch 
d: Doc
d with
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.text: String → Doc
Doc.text 
s: String
s =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_print: Resolve F (Doc.text s) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.text s) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F (Doc.text s) c i (MeasureSet.tainted m)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_widen: Widen (Doc.text s) D

h_bad✝: c + String.length s > F.W ∨ i > F.W

h✝: MeasRender F (Doc.text s) c i m

text_taint
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_print: Resolve F (Doc.text s) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.text s) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mexists 
Doc.text: String → Doc
Doc.text 
s: String
s
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_widen: Widen (Doc.text s) D

h_bad✝: c + String.length s > F.W ∨ i > F.W

h✝: MeasRender F (Doc.text s) c i m

text_taint
Doc.text s ∈ D ∧ MeasRender F (Doc.text s) c i m
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_print: Resolve F (Doc.text s) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.text s) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mconstructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_widen: Widen (Doc.text s) D

h_bad✝: c + String.length s > F.W ∨ i > F.W

h✝: MeasRender F (Doc.text s) c i m

text_taint.left
Doc.text s ∈ D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_widen: Widen (Doc.text s) D

h_bad✝: c + String.length s > F.W ∨ i > F.W

h✝: MeasRender F (Doc.text s) c i m

text_taint.right
MeasRender F (Doc.text s) c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_print: Resolve F (Doc.text s) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.text s) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase left => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_widen: Widen (Doc.text s) D

h_bad✝: c + String.length s > F.W ∨ i > F.W

h✝: MeasRender F (Doc.text s) c i m

Doc.text s ∈ Dcases 
h_widen: Widen (Doc.text s) D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

s: String

h_bad✝: c + String.length s > F.W ∨ i > F.W

h✝: MeasRender F (Doc.text s) c i m

text
Doc.text s ∈ [Doc.text s] 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_widen: Widen (Doc.text s) D

h_bad✝: c + String.length s > F.W ∨ i > F.W

h✝: MeasRender F (Doc.text s) c i m

Doc.text s ∈ Dsimp
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_print: Resolve F (Doc.text s) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.text s) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase right => 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

s: String

h_widen: Widen (Doc.text s) D

h_bad✝: c + String.length s > F.W ∨ i > F.W

h✝: MeasRender F (Doc.text s) c i m

MeasRender F (Doc.text s) c i massumption
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.nl: Doc
Doc.nl =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F Doc.nl c i (MeasureSet.tainted m)

h_widen: Widen Doc.nl D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F Doc.nl c i (MeasureSet.tainted m)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_widen: Widen Doc.nl D

h_bad✝: c > F.W ∨ i > F.W

h✝: MeasRender F Doc.nl c i m

line_taint
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F Doc.nl c i (MeasureSet.tainted m)

h_widen: Widen Doc.nl D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mexists 
Doc.nl: Doc
Doc.nl
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_widen: Widen Doc.nl D

h_bad✝: c > F.W ∨ i > F.W

h✝: MeasRender F Doc.nl c i m

line_taint
Doc.nl ∈ D ∧ MeasRender F Doc.nl c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F Doc.nl c i (MeasureSet.tainted m)

h_widen: Widen Doc.nl D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mconstructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_widen: Widen Doc.nl D

h_bad✝: c > F.W ∨ i > F.W

h✝: MeasRender F Doc.nl c i m

line_taint.left
Doc.nl ∈ D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_widen: Widen Doc.nl D

h_bad✝: c > F.W ∨ i > F.W

h✝: MeasRender F Doc.nl c i m

line_taint.right
MeasRender F Doc.nl c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F Doc.nl c i (MeasureSet.tainted m)

h_widen: Widen Doc.nl D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase left => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_widen: Widen Doc.nl D

h_bad✝: c > F.W ∨ i > F.W

h✝: MeasRender F Doc.nl c i m

Doc.nl ∈ Dcases 
h_widen: Widen Doc.nl D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_bad✝: c > F.W ∨ i > F.W

h✝: MeasRender F Doc.nl c i m

nl
Doc.nl ∈ [Doc.nl] 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_widen: Widen Doc.nl D

h_bad✝: c > F.W ∨ i > F.W

h✝: MeasRender F Doc.nl c i m

Doc.nl ∈ Dsimp
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F Doc.nl c i (MeasureSet.tainted m)

h_widen: Widen Doc.nl D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase right => 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_widen: Widen Doc.nl D

h_bad✝: c > F.W ∨ i > F.W

h✝: MeasRender F Doc.nl c i m

MeasRender F Doc.nl c i massumption
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.nest: ℕ → Doc → Doc
Doc.nest 
n: ℕ
n 
d': Doc
d' =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_print: Resolve F (Doc.nest n d') c i (MeasureSet.tainted m)

h_widen: Widen (Doc.nest n d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mgeneralize h_gen : 
MeasureSet.tainted: {α : Type} → Meas → MeasureSet
MeasureSet.tainted 
_: Meas
_ = ml at 
h_print: Resolve F (Doc.nest n d') c i (MeasureSet.tainted m)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ml: MeasureSet

h_gen: MeasureSet.tainted m = ml

h_print: Resolve F (Doc.nest n d') c i ml

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_print: Resolve F (Doc.nest n d') c i (MeasureSet.tainted m)

h_widen: Widen (Doc.nest n d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F (Doc.nest n d') c i ml
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms✝: MeasureSet

h✝: Resolve F d' c (i + n) ms✝

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) ms✝

nest
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_print: Resolve F (Doc.nest n d') c i (MeasureSet.tainted m)

h_widen: Widen (Doc.nest n d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase nest 
ms': MeasureSet
ms' 
h': Resolve F d' c (i + n) ms'
h' => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms': MeasureSet

h': Resolve F d' c (i + n) ms'

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
ms': MeasureSet
ms'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

tainted
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms': MeasureSet

h': Resolve F d' c (i + n) ms'

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase set => 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c (i + n) (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift] at 
h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set ms✝ h✝)
h_gen
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

ms': MeasureSet

h': Resolve F d' c (i + n) ms'

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase tainted => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift] at 
h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: m = Meas.adjust_nest n m✝

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msubst 
h_gen: m = Meas.adjust_nest n m✝
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i (Meas.adjust_nest n m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_widen: Widen (Doc.nest n d') D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d': Doc

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

L✝: List Doc

h✝: Widen d' L✝

nest
∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_nest n m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mrename_i 
h_widen: Widen d' L✝
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d': Doc

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d' L✝

nest
∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_nest n m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mlet ⟨
d': Doc
d', 
h_in: d' ∈ L✝
h_in, 
h_render: MeasRender F d' c (i + n) m✝
h_render⟩ := 
Resolve_tainted_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas} {D : List Doc},
  Resolve F d c i (MeasureSet.tainted m) →
    Widen d D → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_tainted_valid 
h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)
h' 
h_widen: Widen d' L✝
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d'✝: Doc

m✝: Meas

h': Resolve F d'✝ c (i + n) (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d'✝ L✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c (i + n) m✝

nest
∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_nest n m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mexists 
Doc.nest: ℕ → Doc → Doc
Doc.nest 
n: ℕ
n 
d': Doc
d'
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d'✝: Doc

m✝: Meas

h': Resolve F d'✝ c (i + n) (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d'✝ L✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c (i + n) m✝

nest
Doc.nest n d' ∈ List.map (fun d => Doc.nest n d) L✝ ∧ MeasRender F (Doc.nest n d') c i (Meas.adjust_nest n m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimp [*]
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d'✝: Doc

m✝: Meas

h': Resolve F d'✝ c (i + n) (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d'✝ L✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c (i + n) m✝

nest
MeasRender F (Doc.nest n d') c i (Meas.adjust_nest n m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mhave := 
MeasRender_doc: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas}, MeasRender F d c i m → Choiceless d → m.doc = d
MeasRender_doc 
h_render: MeasRender F d' c (i + n) m✝
h_render (
Widen_choiceless: ∀ {d : Doc} {D : List Doc} {d_choiceless : Doc}, Widen d D → d_choiceless ∈ D → Choiceless d_choiceless
Widen_choiceless 
h_widen: Widen d'✝ L✝
h_widen 
h_in: d' ∈ L✝
h_in)
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d'✝: Doc

m✝: Meas

h': Resolve F d'✝ c (i + n) (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d'✝ L✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c (i + n) m✝

this: m✝.doc = d'

nest
MeasRender F (Doc.nest n d') c i (Meas.adjust_nest n m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msubst 
this: ?m.421449
this
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d': Doc

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d' L✝

h_in: m✝.doc ∈ L✝

h_render: MeasRender F m✝.doc c (i + n) m✝

nest
MeasRender F (Doc.nest n m✝.doc) c i (Meas.adjust_nest n m✝) 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mconstructor
α✝: Type

F: Factory α✝

d: Doc

c, i, n: ℕ

d': Doc

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d' L✝

h_in: m✝.doc ∈ L✝

h_render: MeasRender F m✝.doc c (i + n) m✝

nest.h
MeasRender F m✝.doc c (i + n)
  { last := (Meas.adjust_nest n m✝).last, cost := (Meas.adjust_nest n m✝).cost, doc := m✝.doc,
    x := (Meas.adjust_nest n m✝).x, y := (Meas.adjust_nest n m✝).y }
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

n: ℕ

d': Doc

h_widen: Widen (Doc.nest n d') D

m✝: Meas

h': Resolve F d' c (i + n) (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimpa [
Meas.adjust_nest: {α : Type} → ℕ → Meas → Meas
Meas.adjust_nest]
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.align: Doc → Doc
Doc.align 
d': Doc
d' =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_print: Resolve F (Doc.align d') c i (MeasureSet.tainted m)

h_widen: Widen (Doc.align d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mgeneralize h_gen : 
MeasureSet.tainted: {α : Type} → Meas → MeasureSet
MeasureSet.tainted 
_: Meas
_ = ml at 
h_print: Resolve F (Doc.align d') c i (MeasureSet.tainted m)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

ml: MeasureSet

h_gen: MeasureSet.tainted m = ml

h_print: Resolve F (Doc.align d') c i ml

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_print: Resolve F (Doc.align d') c i (MeasureSet.tainted m)

h_widen: Widen (Doc.align d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F (Doc.align d') c i ml
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

ms✝: MeasureSet

h✝: Resolve F d' c c ms✝

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms✝)

align_taint
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

ms✝: MeasureSet

h✝: Resolve F d' c c ms✝

h_ok✝: i ≤ F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) ms✝

align
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_print: Resolve F (Doc.align d') c i (MeasureSet.tainted m)

h_widen: Widen (Doc.align d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase align 
ms': MeasureSet
ms' 
h': Resolve F d' c c ms'
h' _ => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h': Resolve F d' c c ms'

h_ok✝: i ≤ F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
ms': MeasureSet
ms'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

tainted
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h': Resolve F d' c c ms'

h_ok✝: i ≤ F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase set => 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d' c c (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set ms✝ h✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift] at 
h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set ms✝ h✝)
h_gen
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h': Resolve F d' c c ms'

h_ok✝: i ≤ F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) ms'

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase tainted => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift] at 
h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: m = Meas.adjust_align i m✝

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msubst 
h_gen: m = Meas.adjust_align i m✝
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝) 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_widen: Widen (Doc.align d') D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

L✝: List Doc

h✝: Widen d' L✝

align
∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mrename_i 
h_widen: Widen d' L✝
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d' L✝

align
∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mlet ⟨
d': Doc
d', 
h_in: d' ∈ L✝
h_in, 
h_render: MeasRender F d' c c m✝
h_render⟩ := 
Resolve_tainted_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas} {D : List Doc},
  Resolve F d c i (MeasureSet.tainted m) →
    Widen d D → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_tainted_valid 
h': Resolve F d' c c (MeasureSet.tainted m✝)
h' 
h_widen: Widen d' L✝
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d'✝ c c (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d'✝ L✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m✝

align
∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mexists 
Doc.align: Doc → Doc
Doc.align 
d': Doc
d'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d'✝ c c (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d'✝ L✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m✝

align
Doc.align d' ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F (Doc.align d') c i (Meas.adjust_align i m✝) 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimp [*]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d'✝ c c (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d'✝ L✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m✝

align
MeasRender F (Doc.align d') c i (Meas.adjust_align i m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mhave := 
MeasRender_doc: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas}, MeasRender F d c i m → Choiceless d → m.doc = d
MeasRender_doc 
h_render: MeasRender F d' c c m✝
h_render (
Widen_choiceless: ∀ {d : Doc} {D : List Doc} {d_choiceless : Doc}, Widen d D → d_choiceless ∈ D → Choiceless d_choiceless
Widen_choiceless 
h_widen: Widen d'✝ L✝
h_widen 
h_in: d' ∈ L✝
h_in)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d'✝ c c (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d'✝ L✝

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m✝

this: m✝.doc = d'

align
MeasRender F (Doc.align d') c i (Meas.adjust_align i m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msubst 
this: ?m.428011
this
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d' L✝

h_in: m✝.doc ∈ L✝

h_render: MeasRender F m✝.doc c c m✝

align
MeasRender F (Doc.align m✝.doc) c i (Meas.adjust_align i m✝) 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mconstructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

L✝: List Doc

h_widen: Widen d' L✝

h_in: m✝.doc ∈ L✝

h_render: MeasRender F m✝.doc c c m✝

align.h
MeasRender F m✝.doc c c
  { last := (Meas.adjust_align i m✝).last, cost := (Meas.adjust_align i m✝).cost, doc := m✝.doc,
    x := (Meas.adjust_align i m✝).x, y := m✝.y }
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

h_ok✝: i ≤ F.W

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i msimpa [
Meas.adjust_align: {α : Type} → ℕ → Meas → Meas
Meas.adjust_align]
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_print: Resolve F (Doc.align d') c i (MeasureSet.tainted m)

h_widen: Widen (Doc.align d') D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase align_taint 
ms': MeasureSet
ms' _ _ => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_widen: Widen (Doc.align d') D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

ms': MeasureSet

h✝¹: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

L✝: List Doc

h✝: Widen d' L✝

align
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mrename_i 
h_widen: Widen d' L✝
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

L✝: List Doc

h_widen: Widen d' L✝

align
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
ms': MeasureSet
ms'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h✝: Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint (MeasureSet.tainted m✝))

align.tainted
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

ms✝: List Meas

h✝¹: ms✝ ≠ []

h✝: Resolve F d' c c (MeasureSet.set ms✝ h✝¹)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint (MeasureSet.set ms✝ h✝¹))

align.set
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

L✝: List Doc

h_widen: Widen d' L✝

align
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m<;>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h✝: Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint (MeasureSet.tainted m✝))

align.tainted
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

ms✝: List Meas

h✝¹: ms✝ ≠ []

h✝: Resolve F d' c c (MeasureSet.set ms✝ h✝¹)

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint (MeasureSet.set ms✝ h✝¹))

align.set
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

L✝: List Doc

h_widen: Widen d' L✝

align
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift, 
MeasureSet.taint: {α : Type} → MeasureSet → MeasureSet
MeasureSet.taint] at 
h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint (MeasureSet.set ms✝ h✝¹))
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h✝: Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: m = Meas.adjust_align i m✝

align.tainted
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

L✝: List Doc

h_widen: Widen d' L✝

align
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m<;>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h✝: Resolve F d' c c (MeasureSet.tainted m✝)

h_gen: m = Meas.adjust_align i m✝

align.tainted
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

ms✝: List Meas

h✝¹: ms✝ ≠ []

h✝: Resolve F d' c c (MeasureSet.set ms✝ h✝¹)

h_gen: m = Meas.adjust_align i (List.head ms✝ h✝¹)

align.set
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i m 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d': Doc

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

L✝: List Doc

h_widen: Widen d' L✝

align
∃ d_choiceless, d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i msubst 
h_gen: m = Meas.adjust_align i m✝
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h✝: Resolve F d' c c (MeasureSet.tainted m✝)

align.tainted
∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase tainted 
h': Resolve F d' c c (MeasureSet.tainted m✝)
h' => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)let ⟨
d': Doc
d', 
h_in: d' ∈ L✝
h_in, 
h_render: MeasRender F d' c c m✝
h_render⟩ := 
Resolve_tainted_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas} {D : List Doc},
  Resolve F d c i (MeasureSet.tainted m) →
    Widen d D → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_tainted_valid 
h': Resolve F d' c c (MeasureSet.tainted m✝)
h' 
h_widen: Widen d' L✝
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d'✝ L✝

m✝: Meas

h': Resolve F d'✝ c c (MeasureSet.tainted m✝)

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m✝

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)exists 
Doc.align: Doc → Doc
Doc.align 
d': Doc
d'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d'✝ L✝

m✝: Meas

h': Resolve F d'✝ c c (MeasureSet.tainted m✝)

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m✝

Doc.align d' ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F (Doc.align d') c i (Meas.adjust_align i m✝) 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)simp [*]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d'✝ L✝

m✝: Meas

h': Resolve F d'✝ c c (MeasureSet.tainted m✝)

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m✝

MeasRender F (Doc.align d') c i (Meas.adjust_align i m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)have := 
MeasRender_doc: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas}, MeasRender F d c i m → Choiceless d → m.doc = d
MeasRender_doc 
h_render: MeasRender F d' c c m✝
h_render (
Widen_choiceless: ∀ {d : Doc} {D : List Doc} {d_choiceless : Doc}, Widen d D → d_choiceless ∈ D → Choiceless d_choiceless
Widen_choiceless 
h_widen: Widen d'✝ L✝
h_widen 
h_in: d' ∈ L✝
h_in)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d'✝ L✝

m✝: Meas

h': Resolve F d'✝ c c (MeasureSet.tainted m✝)

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c m✝

this: m✝.doc = d'

MeasRender F (Doc.align d') c i (Meas.adjust_align i m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)subst 
this: ?m.435598
this
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_in: m✝.doc ∈ L✝

h_render: MeasRender F m✝.doc c c m✝

MeasRender F (Doc.align m✝.doc) c i (Meas.adjust_align i m✝) 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)constructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

h_in: m✝.doc ∈ L✝

h_render: MeasRender F m✝.doc c c m✝

h
MeasRender F m✝.doc c c
  { last := (Meas.adjust_align i m✝).last, cost := (Meas.adjust_align i m✝).cost, doc := m✝.doc,
    x := (Meas.adjust_align i m✝).x, y := m✝.y }
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

m✝: Meas

h': Resolve F d' c c (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧ MeasRender F d_choiceless c i (Meas.adjust_align i m✝)simpa [
Meas.adjust_align: {α : Type} → ℕ → Meas → Meas
Meas.adjust_align]
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d': Doc

h_widen: Widen (Doc.align d') D

ms': MeasureSet

h✝: Resolve F d' c c ms'

h_bad✝: i > F.W

h_gen: MeasureSet.tainted m = MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms')

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase set 
ms_res: List Meas
ms_res 
h_non_empty: ms_res ≠ []
h_non_empty 
h': Resolve F d' c c (MeasureSet.set ms_res h_non_empty)
h' => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

ms_res: List Meas

h_non_empty: ms_res ≠ []

h': Resolve F d' c c (MeasureSet.set ms_res h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head ms_res h_non_empty))cases 
ms_res: List Meas
ms_res
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

h_non_empty: [] ≠ []

h': Resolve F d' c c (MeasureSet.set [] h_non_empty)

nil
∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head [] h_non_empty))
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

head✝: Meas

tail✝: List Meas

h_non_empty: head✝ :: tail✝ ≠ []

h': Resolve F d' c c (MeasureSet.set (head✝ :: tail✝) h_non_empty)

cons
∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head (head✝ :: tail✝) h_non_empty)) 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

ms_res: List Meas

h_non_empty: ms_res ≠ []

h': Resolve F d' c c (MeasureSet.set ms_res h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head ms_res h_non_empty))case nil => 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

h_non_empty: [] ≠ []

h': Resolve F d' c c (MeasureSet.set [] h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head [] h_non_empty))contradiction
Goals accomplished! 🐙 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

ms_res: List Meas

h_non_empty: ms_res ≠ []

h': Resolve F d' c c (MeasureSet.set ms_res h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head ms_res h_non_empty))case cons 
hd: ?m.436287
hd 
tl: List ?m.436287
tl => 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head (hd :: tl) h_non_empty))have 
h_mem: hd ∈ hd :: tl
h_mem : 
hd: ?m.436287
hd ∈ 
hd: ?m.436287
hd :: 
tl: List ?m.436287
tl := 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head (hd :: tl) h_non_empty))by
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

hd ∈ hd :: tlsimp
Goals accomplished! 🐙
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head (hd :: tl) h_non_empty))let ⟨
d': Doc
d', 
h_in: d' ∈ L✝
h_in, 
h_render: MeasRender F d' c c hd
h_render⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)
h' 
h_widen: Widen d' L✝
h_widen 
h_mem: hd ∈ hd :: tl
h_mem
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d'✝ L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d'✝ c c (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c hd

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head (hd :: tl) h_non_empty))
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head (hd :: tl) h_non_empty))exists 
Doc.align: Doc → Doc
Doc.align 
d': Doc
d'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d'✝ L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d'✝ c c (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c hd

Doc.align d' ∈ List.map (fun d => Doc.align d) L✝ ∧   MeasRender F (Doc.align d') c i (Meas.adjust_align i (List.head (hd :: tl) h_non_empty)) 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head (hd :: tl) h_non_empty))simp [*]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d'✝ L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d'✝ c c (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c hd

MeasRender F (Doc.align d') c i (Meas.adjust_align i hd)
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head (hd :: tl) h_non_empty))have := 
MeasRender_doc: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas}, MeasRender F d c i m → Choiceless d → m.doc = d
MeasRender_doc 
h_render: MeasRender F d' c c hd
h_render (
Widen_choiceless: ∀ {d : Doc} {D : List Doc} {d_choiceless : Doc}, Widen d D → d_choiceless ∈ D → Choiceless d_choiceless
Widen_choiceless 
h_widen: Widen d'✝ L✝
h_widen 
h_in: d' ∈ L✝
h_in)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d'✝: Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d'✝ L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d'✝ c c (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d': Doc

h_in: d' ∈ L✝

h_render: MeasRender F d' c c hd

this: hd.doc = d'

MeasRender F (Doc.align d') c i (Meas.adjust_align i hd)
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head (hd :: tl) h_non_empty))subst 
this: ?m.444602
this
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

h_in: hd.doc ∈ L✝

h_render: MeasRender F hd.doc c c hd

MeasRender F (Doc.align hd.doc) c i (Meas.adjust_align i hd) 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head (hd :: tl) h_non_empty))constructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

h_in: hd.doc ∈ L✝

h_render: MeasRender F hd.doc c c hd

h
MeasRender F hd.doc c c
  { last := (Meas.adjust_align i hd).last, cost := (Meas.adjust_align i hd).cost, doc := hd.doc,
    x := (Meas.adjust_align i hd).x, y := hd.y }
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d': Doc

h_bad✝: i > F.W

L✝: List Doc

h_widen: Widen d' L✝

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h': Resolve F d' c c (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.map (fun d => Doc.align d) L✝ ∧     MeasRender F d_choiceless c i (Meas.adjust_align i (List.head (hd :: tl) h_non_empty))simpa [
Meas.adjust_align: {α : Type} → ℕ → Meas → Meas
Meas.adjust_align]
Goals accomplished! 🐙
          
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.choice: Doc → Doc → Doc
Doc.choice 
d₁: Doc
d₁ 
d₂: Doc
d₂ =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.choice d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mgeneralize h_gen : 
MeasureSet.tainted: {α : Type} → Meas → MeasureSet
MeasureSet.tainted 
_: Meas
_ = ml at 
h_print: Resolve F (Doc.choice d₁ d₂) c i (MeasureSet.tainted m)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d₁, d₂: Doc

h_widen: Widen (Doc.choice d₁ d₂) D

ml: MeasureSet

h_gen: MeasureSet.tainted m = ml

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.choice d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_widen: Widen (Doc.choice d₁ d₂) D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

ml: MeasureSet

h_gen: MeasureSet.tainted m = ml

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

choice
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.choice d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase choice 
h_widen₁: Widen d₁ L₁✝
h_widen₁ 
h_widen₂: Widen d₂ L₂✝
h_widen₂ =>
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

ml: MeasureSet

h_gen: MeasureSet.tainted m = ml

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F (Doc.choice d₁ d₂) c i ml
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝, ms'✝: MeasureSet

h_left✝: Resolve F d₁ c i ms✝

h_right✝: Resolve F d₂ c i ms'✝

h_gen: MeasureSet.tainted m = MeasureSet.union F ms✝ ms'✝

choice
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

ml: MeasureSet

h_gen: MeasureSet.tainted m = ml

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase choice 
ms₁: MeasureSet
ms₁ 
ms₂: MeasureSet
ms₂ 
h₁: Resolve F d₁ c i ms₁
h₁ 
h₂: Resolve F d₂ c i ms₂
h₂ => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₁, ms₂: MeasureSet

h₁: Resolve F d₁ c i ms₁

h₂: Resolve F d₂ c i ms₂

h_gen: MeasureSet.tainted m = MeasureSet.union F ms₁ ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcases 
ms₁: MeasureSet
ms₁
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝) ms₂

tainted
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂

set
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₁, ms₂: MeasureSet

h₁: Resolve F d₁ c i ms₁

h₂: Resolve F d₂ c i ms₂

h_gen: MeasureSet.tainted m = MeasureSet.union F ms₁ ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase tainted => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mdwi { 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcases 
ms₂: MeasureSet
ms₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝¹) (MeasureSet.tainted m✝)

tainted
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m }
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝¹) (MeasureSet.tainted m✝)

tainted
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

m✝: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase tainted => 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝¹) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union] at 
h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝¹) (MeasureSet.tainted m✝)
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: m = m✝¹

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝¹) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msubst 
h_gen: m = m✝¹
h_gen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h₁: Resolve F d₁ c i (MeasureSet.tainted m)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝¹) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mlet ⟨
d': Doc
d', 
h_in: d' ∈ L₁✝
h_in, 
h_render: MeasRender F d' c i m
h_render⟩ := 
Resolve_tainted_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas} {D : List Doc},
  Resolve F d c i (MeasureSet.tainted m) →
    Widen d D → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_tainted_valid 
h₁: Resolve F d₁ c i (MeasureSet.tainted m)
h₁ 
h_widen₁: Widen d₁ L₁✝
h_widen₁
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h₁: Resolve F d₁ c i (MeasureSet.tainted m)

d': Doc

h_in: d' ∈ L₁✝

h_render: MeasRender F d' c i m

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝¹) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mexists 
d': Doc
d'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h₁: Resolve F d₁ c i (MeasureSet.tainted m)

d': Doc

h_in: d' ∈ L₁✝

h_render: MeasRender F d' c i m

d' ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d' c i m 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h₁: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝¹) (MeasureSet.tainted m✝)

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp [
h_in: d' ∈ L₁✝
h_in, 
h_render: MeasRender F d' c i m
h_render]
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₁, ms₂: MeasureSet

h₁: Resolve F d₁ c i ms₁

h₂: Resolve F d₂ c i ms₂

h_gen: MeasureSet.tainted m = MeasureSet.union F ms₁ ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcase set 
ms': List Meas
ms' _ => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms' h✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i mcases 
ms₂: MeasureSet
ms₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms' h✝) (MeasureSet.tainted m✝)

tainted
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms' h✝¹) (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms' h✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m<;>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

m✝: Meas

h₂: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms' h✝) (MeasureSet.tainted m✝)

tainted
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms': List Meas

h✝¹: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h₂: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms' h✝¹) (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i m 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h₂: Resolve F d₂ c i ms₂

ms': List Meas

h✝: ms' ≠ []

h₁: Resolve F d₁ c i (MeasureSet.set ms' h✝)

h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms' h✝) ms₂

∃ d_choiceless, d_choiceless ∈ L₁✝ ++ L₂✝ ∧ MeasRender F d_choiceless c i msimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union] at 
h_gen: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms' h✝¹) (MeasureSet.set ms✝ h✝)
h_gen
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m| 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d₁: Doc
d₁ 
d₂: Doc
d₂ =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.concat d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

h_print: Resolve F d c i (MeasureSet.tainted m)

h_widen: Widen d D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_widen: Widen (Doc.concat d₁ d₂) D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.tainted m)

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

concat
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i m
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.concat d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mrename_i 
h_widen₁: Widen d₁ L₁✝
h_widen₁ 
h_widen₂: Widen d₂ L₂✝
h_widen₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.tainted m)

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

concat
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i m
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.concat d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcases 
h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.tainted m)
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint✝: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right✝: Resolve F d₂ m✝.last i ms'✝

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝)

concat.concat_taint
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

concat.concat_set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i m
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.concat d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase concat_taint 
ms: MeasureSet
ms _ 
h_taint: MeasureSet.taint ms = MeasureSet.tainted m'✝
h_taint 
h_right: Resolve F d₂ m✝.last i ms
h_right 
h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)
h_left => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

ms: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms = MeasureSet.tainted m'✝

h_right: Resolve F d₂ m✝.last i ms

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝)cases 
ms: MeasureSet
ms
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹, m'✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_taint: MeasureSet.taint (MeasureSet.tainted m✝) = MeasureSet.tainted m'✝

h_right: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝¹ m'✝)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝, m'✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h_taint: MeasureSet.taint (MeasureSet.set ms✝ h✝) = MeasureSet.tainted m'✝

h_right: Resolve F d₂ m✝.last i (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝) 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

ms: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms = MeasureSet.tainted m'✝

h_right: Resolve F d₂ m✝.last i ms

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝)<;>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹, m'✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_taint: MeasureSet.taint (MeasureSet.tainted m✝) = MeasureSet.tainted m'✝

h_right: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝¹ m'✝)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝, m'✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h_taint: MeasureSet.taint (MeasureSet.set ms✝ h✝) = MeasureSet.tainted m'✝

h_right: Resolve F d₂ m✝.last i (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝) 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

ms: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms = MeasureSet.tainted m'✝

h_right: Resolve F d₂ m✝.last i ms

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝)simp [
MeasureSet.taint: {α : Type} → MeasureSet → MeasureSet
MeasureSet.taint] at 
h_taint: MeasureSet.taint (MeasureSet.tainted m✝) = MeasureSet.tainted m'✝
h_taint
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹, m'✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

h_taint: m✝ = m'✝

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝¹ m'✝) 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

ms: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms = MeasureSet.tainted m'✝

h_right: Resolve F d₂ m✝.last i ms

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝)<;>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹, m'✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

h_taint: m✝ = m'✝

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝¹ m'✝)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝, m'✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set ms✝ h✝)

h_taint: List.head ms✝ h✝ = m'✝

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝) 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

ms: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms = MeasureSet.tainted m'✝

h_right: Resolve F d₂ m✝.last i ms

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝)subst 
h_taint: m✝ = m'✝
h_taint
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head ms✝ h✝))
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

ms: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms = MeasureSet.tainted m'✝

h_right: Resolve F d₂ m✝.last i ms

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝)case tainted => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝¹ m✝)let ⟨
d_left: Doc
d_left, _, 
h_left: MeasRender F d_left c i m✝¹
h_left⟩ := 
Resolve_tainted_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas} {D : List Doc},
  Resolve F d c i (MeasureSet.tainted m) →
    Widen d D → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_tainted_valid 
h_left: Resolve F d₁ c i (MeasureSet.tainted m✝¹)
h_left 
h_widen₁: Widen d₁ L₁✝
h_widen₁
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

d_left: Doc

left✝: d_left ∈ L₁✝

h_left: MeasRender F d_left c i m✝¹

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝¹ m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝¹ m✝)let ⟨
d_right: Doc
d_right, _, 
h_right: MeasRender F d_right m✝¹.last i m✝
h_right⟩ := 
Resolve_tainted_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas} {D : List Doc},
  Resolve F d c i (MeasureSet.tainted m) →
    Widen d D → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_tainted_valid 
h_right: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)
h_right 
h_widen₂: Widen d₂ L₂✝
h_widen₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right✝: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

d_left: Doc

left✝¹: d_left ∈ L₁✝

h_left: MeasRender F d_left c i m✝¹

d_right: Doc

left✝: d_right ∈ L₂✝

h_right: MeasRender F d_right m✝¹.last i m✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝¹ m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝¹ m✝)exists 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d_left: Doc
d_left 
d_right: Doc
d_right
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right✝: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

d_left: Doc

left✝¹: d_left ∈ L₁✝

h_left: MeasRender F d_left c i m✝¹

d_right: Doc

left✝: d_right ∈ L₂✝

h_right: MeasRender F d_right m✝¹.last i m✝

Doc.concat d_left d_right ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧   MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m✝¹ m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝¹ m✝)simp [*]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right✝: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

d_left: Doc

left✝¹: d_left ∈ L₁✝

h_left: MeasRender F d_left c i m✝¹

d_right: Doc

left✝: d_right ∈ L₂✝

h_right: MeasRender F d_right m✝¹.last i m✝

MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m✝¹ m✝)
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝¹ m✝)dwi { 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right✝: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

d_left: Doc

left✝¹: d_left ∈ L₁✝

h_left: MeasRender F d_left c i m✝¹

d_right: Doc

left✝: d_right ∈ L₂✝

h_right: MeasRender F d_right m✝¹.last i m✝

MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m✝¹ m✝)constructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right✝: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

d_left: Doc

left✝¹: d_left ∈ L₁✝

h_left: MeasRender F d_left c i m✝¹

d_right: Doc

left✝: d_right ∈ L₂✝

h_right: MeasRender F d_right m✝¹.last i m✝

h₁
MeasRender F d_left c i ?m₁
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right✝: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

d_left: Doc

left✝¹: d_left ∈ L₁✝

h_left: MeasRender F d_left c i m✝¹

d_right: Doc

left✝: d_right ∈ L₂✝

h_right: MeasRender F d_right m✝¹.last i m✝

h₂
MeasRender F d_right ?m₁.last i ?m₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right✝: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

d_left: Doc

left✝¹: d_left ∈ L₁✝

h_left: MeasRender F d_left c i m✝¹

d_right: Doc

left✝: d_right ∈ L₂✝

h_right: MeasRender F d_right m✝¹.last i m✝

h
Meas.concat F m✝¹ m✝ = Meas.concat F ?m₁ ?m₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right✝: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

d_left: Doc

left✝¹: d_left ∈ L₁✝

h_left: MeasRender F d_left c i m✝¹

d_right: Doc

left✝: d_right ∈ L₂✝

h_right: MeasRender F d_right m✝¹.last i m✝

m₁
Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝¹: Meas

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝¹)

m✝: Meas

h_right✝: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m✝)

d_left: Doc

left✝¹: d_left ∈ L₁✝

h_left: MeasRender F d_left c i m✝¹

d_right: Doc

left✝: d_right ∈ L₂✝

h_right: MeasRender F d_right m✝¹.last i m✝

m₂
Meas }
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

ms: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms = MeasureSet.tainted m'✝

h_right: Resolve F d₂ m✝.last i ms

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝)case set 
ms_res: List Meas
ms_res 
h_non_empty: ms_res ≠ []
h_non_empty => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms_res: List Meas

h_non_empty: ms_res ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set ms_res h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head ms_res h_non_empty))cases 
ms_res: List Meas
ms_res
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_non_empty: [] ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set [] h_non_empty)

nil
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head [] h_non_empty))
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

head✝: Meas

tail✝: List Meas

h_non_empty: head✝ :: tail✝ ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (head✝ :: tail✝) h_non_empty)

cons
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head (head✝ :: tail✝) h_non_empty)) 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms_res: List Meas

h_non_empty: ms_res ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set ms_res h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head ms_res h_non_empty))case nil => 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_non_empty: [] ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set [] h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head [] h_non_empty))contradiction
Goals accomplished! 🐙
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

ms_res: List Meas

h_non_empty: ms_res ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set ms_res h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head ms_res h_non_empty))case cons 
hd: ?m.486414
hd 
tl: List ?m.486414
tl => 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head (hd :: tl) h_non_empty))have 
h_mem: hd ∈ hd :: tl
h_mem : 
hd: ?m.486414
hd ∈ 
hd: ?m.486414
hd :: 
tl: List ?m.486414
tl := 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head (hd :: tl) h_non_empty))by
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

hd ∈ hd :: tlsimp
Goals accomplished! 🐙
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head (hd :: tl) h_non_empty))let ⟨
d_left: Doc
d_left, _, _⟩ := 
Resolve_tainted_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas} {D : List Doc},
  Resolve F d c i (MeasureSet.tainted m) →
    Widen d D → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_tainted_valid 
h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)
h_left 
h_widen₁: Widen d₁ L₁✝
h_widen₁
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d_left: Doc

left✝: d_left ∈ L₁✝

right✝: MeasRender F d_left c i m✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head (hd :: tl) h_non_empty))
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head (hd :: tl) h_non_empty))let ⟨
d_right: Doc
d_right, _, _⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)
h_right 
h_widen₂: Widen d₂ L₂✝
h_widen₂ 
h_mem: hd ∈ hd :: tl
h_mem
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d_left: Doc

left✝¹: d_left ∈ L₁✝

right✝¹: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂✝

right✝: MeasRender F d_right m✝.last i hd

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head (hd :: tl) h_non_empty))
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head (hd :: tl) h_non_empty))exists 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d_left: Doc
d_left 
d_right: Doc
d_right
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d_left: Doc

left✝¹: d_left ∈ L₁✝

right✝¹: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂✝

right✝: MeasRender F d_right m✝.last i hd

Doc.concat d_left d_right ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧   MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m✝ (List.head (hd :: tl) h_non_empty))
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head (hd :: tl) h_non_empty))simp [*]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d_left: Doc

left✝¹: d_left ∈ L₁✝

right✝¹: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂✝

right✝: MeasRender F d_right m✝.last i hd

MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m✝ hd)
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ (List.head (hd :: tl) h_non_empty))dwi { 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d_left: Doc

left✝¹: d_left ∈ L₁✝

right✝¹: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂✝

right✝: MeasRender F d_right m✝.last i hd

MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m✝ hd)constructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d_left: Doc

left✝¹: d_left ∈ L₁✝

right✝¹: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂✝

right✝: MeasRender F d_right m✝.last i hd

h₁
MeasRender F d_left c i ?m₁
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d_left: Doc

left✝¹: d_left ∈ L₁✝

right✝¹: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂✝

right✝: MeasRender F d_right m✝.last i hd

h₂
MeasRender F d_right ?m₁.last i ?m₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d_left: Doc

left✝¹: d_left ∈ L₁✝

right✝¹: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂✝

right✝: MeasRender F d_right m✝.last i hd

h
Meas.concat F m✝ hd = Meas.concat F ?m₁ ?m₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d_left: Doc

left✝¹: d_left ∈ L₁✝

right✝¹: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂✝

right✝: MeasRender F d_right m✝.last i hd

m₁
Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

hd: Meas

tl: List Meas

h_non_empty: hd :: tl ≠ []

h_right: Resolve F d₂ m✝.last i (MeasureSet.set (hd :: tl) h_non_empty)

h_mem: hd ∈ hd :: tl

d_left: Doc

left✝¹: d_left ∈ L₁✝

right✝¹: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂✝

right✝: MeasRender F d_right m✝.last i hd

m₂
Meas }
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

D: List Doc

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i (MeasureSet.tainted m)

h_widen: Widen (Doc.concat d₁ d₂) D

∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i mcase concat_set 
h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)
h_left 
h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)
h_print => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i mdwi { 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝) ∧     MeasRender F d_choiceless c i mapply 
ResolveConcat_tainted_valid: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d₂ : Doc} {i : ℕ} {m : Meas} {d₁ : Doc} {L₁ L₂ : List Doc} {c : ℕ}
  {orig_ms : List Meas} {h_non_empty : orig_ms ≠ []},
  ResolveConcat F ms d₂ i (MeasureSet.tainted m) →
    Widen d₁ L₁ →
      Widen d₂ L₂ →
        Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty) →
          (∀ (x : Meas), x ∈ ms → x ∈ orig_ms) →
            ∃ d_choiceless,
              d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧                 MeasRender F d_choiceless c i m
ResolveConcat_tainted_valid
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

h_right
ResolveConcat F ?ms ?d₂ i (MeasureSet.tainted m)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

h_widen₁
Widen ?d₁ L₁✝
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

h_widen₂
Widen ?d₂ L₂✝
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

h_left
Resolve F ?d₁ c i (MeasureSet.set ?orig_ms ?h_non_empty)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

h_transfer
∀ (x : Meas), x ∈ ?ms → x ∈ ?orig_ms
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

ms
List Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

d₂
Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

d₁
Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

orig_ms
List Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h_print: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m)

h_non_empty
?orig_ms ≠ [] }
Goals accomplished! 🐙
        
  theorem 
ResolveConcat_tainted_valid: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d₂ : Doc} {i : ℕ} {m : Meas} {d₁ : Doc} {L₁ L₂ : List Doc} {c : ℕ}
  {orig_ms : List Meas} {h_non_empty : orig_ms ≠ []},
  ResolveConcat F ms d₂ i (MeasureSet.tainted m) →
    Widen d₁ L₁ →
      Widen d₂ L₂ →
        Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty) →
          (∀ (x : Meas), x ∈ ms → x ∈ orig_ms) →
            ∃ d_choiceless,
              d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧                 MeasRender F d_choiceless c i m
ResolveConcat_tainted_valid 
      (
h_right: ResolveConcat F ms d₂ i (MeasureSet.tainted m)
h_right : 
ResolveConcat: {α : Type} → Factory α → List Meas → Doc → ℕ → MeasureSet → Prop
ResolveConcat 
F: ?m.410464
F 
ms: ?m.410471
ms 
d₂: ?m.410478
d₂ 
i: ?m.410484
i (
MeasureSet.tainted: {α : Type} → Meas → MeasureSet
MeasureSet.tainted 
m: ?m.410493
m)) 
      (
h_widen₁: Widen d₁ L₁
h_widen₁ : 
Widen: Doc → List Doc → Prop
Widen 
d₁: ?m.410504
d₁ 
L₁: ?m.410514
L₁) (
h_widen₂: Widen d₂ L₂
h_widen₂ : 
Widen: Doc → List Doc → Prop
Widen 
d₂: ?m.410478
d₂ 
L₂: ?m.410526
L₂)
      (
h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)
h_left : 
Resolve: {α : Type} → Factory α → Doc → ℕ → ℕ → MeasureSet → Prop
Resolve 
F: ?m.410464
F 
d₁: ?m.410504
d₁ 
c: ?m.410541
c 
i: ?m.410484
i (
MeasureSet.set: {α : Type} → (ms : List Meas) → ms ≠ [] → MeasureSet
MeasureSet.set 
orig_ms: ?m.410558
orig_ms 
h_non_empty: ?m.410575
h_non_empty))
      (
h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms
h_transfer : ∀ 
x: ?m.410597
x, 
x: ?m.410597
x ∈ 
ms: ?m.410471
ms → 
x: ?m.410597
x ∈ 
orig_ms: ?m.410558
orig_ms) :
      ∃ 
d_choiceless: ?m.410656
d_choiceless,
        
d_choiceless: ?m.410656
d_choiceless ∈ 
List.join: {α : Type ?u.410663} → List (List α) → List α
List.join (
List.map: {α : Type ?u.410666} → {β : Type ?u.410665} → (α → β) → List α → List β
List.map (fun 
d₁: ?m.410671
d₁ => 
List.map: {α : Type ?u.410674} → {β : Type ?u.410673} → (α → β) → List α → List β
List.map (fun 
d₂: ?m.410679
d₂ => 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d₁: ?m.410671
d₁ 
d₂: ?m.410679
d₂) 
L₂: ?m.410526
L₂) 
L₁: ?m.410514
L₁) ∧ 
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: ?m.410464
F  
d_choiceless: ?m.410656
d_choiceless 
c: ?m.410541
c 
i: ?m.410484
i 
m: ?m.410493
m := by
Goals accomplished! 🐙 
    
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_right: ResolveConcat F ms d₂ i (MeasureSet.tainted m)

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mgeneralize h_ml : 
MeasureSet.tainted: {α : Type} → Meas → MeasureSet
MeasureSet.tainted 
_: Meas
_ = ml at 
h_right: ResolveConcat F ms d₂ i (MeasureSet.tainted m)
h_right
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

ml: MeasureSet

h_ml: MeasureSet.tainted m = ml

h_right: ResolveConcat F ms d₂ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
    
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_right: ResolveConcat F ms d₂ i (MeasureSet.tainted m)

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
h_right: ResolveConcat F ms d₂ i ml
h_right
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ml: MeasureSet

h_ml: MeasureSet.tainted m = ml

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

h_current✝: ResolveConcatOne F d₂ m✝ i ml

one
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

msr✝: MeasureSet

m✝: Meas

msr'✝: MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝ :: ms✝ → x ∈ orig_ms

h_rest✝: ResolveConcat F ms✝ d₂ i msr✝

h_current✝: ResolveConcatOne F d₂ m✝ i msr'✝

h_ml: MeasureSet.tainted m = MeasureSet.union F msr'✝ msr✝

cons
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
    
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_right: ResolveConcat F ms d₂ i (MeasureSet.tainted m)

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase one 
h_current: ResolveConcatOne F d₂ m✝ i ml
h_current =>
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ml: MeasureSet

h_ml: MeasureSet.tainted m = ml

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m✝ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
h_current: ResolveConcatOne F d₂ m✝ i ml
h_current
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

m'✝: Meas

h✝: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m = MeasureSet.tainted (Meas.concat F m✝ m'✝)

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h✝: Resolve F d₂ m✝.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.tainted m =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m✝ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m✝ m') ms✝) ≠ [])

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ml: MeasureSet

h_ml: MeasureSet.tainted m = ml

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m✝ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase set => 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h✝: Resolve F d₂ m✝.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.tainted m =   MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m✝ m') ms✝))
    (_ : dedup F (List.map (fun m' => Meas.concat F m✝ m') ms✝) ≠ [])

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcontradiction
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ml: MeasureSet

h_ml: MeasureSet.tainted m = ml

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m✝ i ml

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase tainted 
h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)
h_current => 
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m = MeasureSet.tainted (Meas.concat F m✝ m'✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp at 
h_ml: MeasureSet.tainted m = MeasureSet.tainted (Meas.concat F m✝ m'✝)
h_ml 
h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms
h_transfer
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_ml: m = Meas.concat F m✝ m'✝

h_transfer: m✝ ∈ orig_ms

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m = MeasureSet.tainted (Meas.concat F m✝ m'✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msubst 
h_ml: m = Meas.concat F m✝ m'✝
h_ml
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_transfer: m✝ ∈ orig_ms

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝)
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m = MeasureSet.tainted (Meas.concat F m✝ m'✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
d_left: Doc
d_left, _, 
h₁: MeasRender F d_left c i m✝
h₁⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)
h_left 
h_widen₁: Widen d₁ L₁
h_widen₁ 
h_transfer: m✝ ∈ orig_ms
h_transfer
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_transfer: m✝ ∈ orig_ms

d_left: Doc

left✝: d_left ∈ L₁

h₁: MeasRender F d_left c i m✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝)
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m = MeasureSet.tainted (Meas.concat F m✝ m'✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mlet ⟨
d_right: Doc
d_right, _, 
h₂: MeasRender F d_right m✝.last i m'✝
h₂⟩ := 
Resolve_tainted_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas} {D : List Doc},
  Resolve F d c i (MeasureSet.tainted m) →
    Widen d D → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_tainted_valid 
h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)
h_current 
h_widen₂: Widen d₂ L₂
h_widen₂
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_transfer: m✝ ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m✝.last i m'✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i (Meas.concat F m✝ m'✝)
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m = MeasureSet.tainted (Meas.concat F m✝ m'✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mexists 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d_left: Doc
d_left 
d_right: Doc
d_right
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_transfer: m✝ ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m✝.last i m'✝

Doc.concat d_left d_right ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧   MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m✝ m'✝)
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m = MeasureSet.tainted (Meas.concat F m✝ m'✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp [*]
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_transfer: m✝ ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m✝.last i m'✝

MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m✝ m'✝)
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ [m✝] → x ∈ orig_ms

m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m = MeasureSet.tainted (Meas.concat F m✝ m'✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mdwi { 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_transfer: m✝ ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m✝.last i m'✝

MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m✝ m'✝)constructor
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_transfer: m✝ ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m✝.last i m'✝

h₁
MeasRender F d_left c i ?m₁
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_transfer: m✝ ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m✝.last i m'✝

h₂
MeasRender F d_right ?m₁.last i ?m₂
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_transfer: m✝ ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m✝.last i m'✝

h
Meas.concat F m✝ m'✝ = Meas.concat F ?m₁ ?m₂
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_transfer: m✝ ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m✝.last i m'✝

m₁
Meas
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

m✝, m'✝: Meas

h_current: Resolve F d₂ m✝.last i (MeasureSet.tainted m'✝)

h_transfer: m✝ ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m✝

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m✝.last i m'✝

m₂
Meas }
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_right: ResolveConcat F ms d₂ i (MeasureSet.tainted m)

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

h_transfer: ∀ (x : Meas), x ∈ ms → x ∈ orig_ms

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase cons 
msr: MeasureSet
msr _ 
msr': MeasureSet
msr' 
h_rest: ResolveConcat F ms✝ d₂ i msr
h_rest 
h_current: ResolveConcatOne F d₂ m✝ i msr'
h_current => 
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

msr: MeasureSet

m✝: Meas

msr': MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝ :: ms✝ → x ∈ orig_ms

h_rest: ResolveConcat F ms✝ d₂ i msr

h_current: ResolveConcatOne F d₂ m✝ i msr'

h_ml: MeasureSet.tainted m = MeasureSet.union F msr' msr

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
msr: MeasureSet
msr
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m✝¹: Meas

msr': MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝¹ :: ms✝ → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m✝¹ i msr'

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F msr' (MeasureSet.tainted m✝)

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝¹: List Meas

m✝: Meas

msr': MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝ :: ms✝¹ → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m✝ i msr'

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F msr' (MeasureSet.set ms✝ h✝)

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

msr: MeasureSet

m✝: Meas

msr': MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝ :: ms✝ → x ∈ orig_ms

h_rest: ResolveConcat F ms✝ d₂ i msr

h_current: ResolveConcatOne F d₂ m✝ i msr'

h_ml: MeasureSet.tainted m = MeasureSet.union F msr' msr

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase tainted => 
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m✝¹: Meas

msr': MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝¹ :: ms✝ → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m✝¹ i msr'

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F msr' (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
h_current: ResolveConcatOne F d₂ m✝¹ i msr'
h_current
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m✝¹: Meas

h_transfer: ∀ (x : Meas), x ∈ m✝¹ :: ms✝ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h✝: Resolve F d₂ m✝¹.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m✝¹ m'✝)) (MeasureSet.tainted m✝)

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝¹: List Meas

m✝¹: Meas

h_transfer: ∀ (x : Meas), x ∈ m✝¹ :: ms✝¹ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h✝: Resolve F d₂ m✝¹.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.tainted m =   MeasureSet.union F
    (MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m✝¹ m') ms✝))
      (_ : dedup F (List.map (fun m' => Meas.concat F m✝¹ m') ms✝) ≠ []))
    (MeasureSet.tainted m✝)

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m✝¹: Meas

msr': MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝¹ :: ms✝ → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m✝¹ i msr'

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F msr' (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase set => 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝¹: List Meas

m✝¹: Meas

h_transfer: ∀ (x : Meas), x ∈ m✝¹ :: ms✝¹ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.tainted m✝)

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h✝: Resolve F d₂ m✝¹.last i (MeasureSet.set ms✝ h_non_empty✝)

h_ml: MeasureSet.tainted m =   MeasureSet.union F
    (MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m✝¹ m') ms✝))
      (_ : dedup F (List.map (fun m' => Meas.concat F m✝¹ m') ms✝) ≠ []))
    (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcontradiction
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m✝¹: Meas

msr': MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝¹ :: ms✝ → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m✝¹ i msr'

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F msr' (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase tainted 
m: Meas
m _ _ 
h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)
h_current => 
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m: Meas

h_transfer: ∀ (x : Meas), x ∈ m :: ms✝ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m✝¹specialize 
h_transfer: ∀ (x : Meas), x ∈ m :: ms✝ → x ∈ orig_ms
h_transfer 
m: Meas
m (
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m: Meas

h_transfer: ∀ (x : Meas), x ∈ m :: ms✝ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m✝¹by
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m: Meas

h_transfer: ∀ (x : Meas), x ∈ m :: ms✝ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)

m ∈ m :: ms✝simp
Goals accomplished! 🐙)
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)

h_transfer: m ∈ orig_ms

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m✝¹
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m: Meas

h_transfer: ∀ (x : Meas), x ∈ m :: ms✝ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m✝¹simp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union] at 
h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)
h_ml
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

h_ml: m✝¹ = Meas.concat F m m'✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m✝¹
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m: Meas

h_transfer: ∀ (x : Meas), x ∈ m :: ms✝ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m✝¹subst 
h_ml: m✝¹ = Meas.concat F m m'✝
h_ml
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i (Meas.concat F m m'✝)
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m: Meas

h_transfer: ∀ (x : Meas), x ∈ m :: ms✝ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m✝¹let ⟨
d_left: Doc
d_left, _, 
h₁: MeasRender F d_left c i m
h₁⟩ := 
Resolve_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h : ms ≠ []} {D : List Doc} {m : Meas},
  Resolve F d c i (MeasureSet.set ms h) →
    Widen d D → m ∈ ms → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_valid 
h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)
h_left 
h_widen₁: Widen d₁ L₁
h_widen₁ 
h_transfer: m ∈ orig_ms
h_transfer
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

d_left: Doc

left✝: d_left ∈ L₁

h₁: MeasRender F d_left c i m

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i (Meas.concat F m m'✝)
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m: Meas

h_transfer: ∀ (x : Meas), x ∈ m :: ms✝ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m✝¹let ⟨
d_right: Doc
d_right, _, 
h₂: MeasRender F d_right m.last i m'✝
h₂⟩ := 
Resolve_tainted_valid: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {m : Meas} {D : List Doc},
  Resolve F d c i (MeasureSet.tainted m) →
    Widen d D → ∃ d_choiceless, d_choiceless ∈ D ∧ MeasRender F d_choiceless c i m
Resolve_tainted_valid 
h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)
h_current 
h_widen₂: Widen d₂ L₂
h_widen₂
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m.last i m'✝

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i (Meas.concat F m m'✝)
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m: Meas

h_transfer: ∀ (x : Meas), x ∈ m :: ms✝ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m✝¹exists 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d_left: Doc
d_left 
d_right: Doc
d_right
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m.last i m'✝

Doc.concat d_left d_right ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧   MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m m'✝)
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m: Meas

h_transfer: ∀ (x : Meas), x ∈ m :: ms✝ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m✝¹simp [*]
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m.last i m'✝

MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m m'✝)
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m✝¹: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m: Meas

h_transfer: ∀ (x : Meas), x ∈ m :: ms✝ → x ∈ orig_ms

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_ml: MeasureSet.tainted m✝¹ = MeasureSet.union F (MeasureSet.tainted (Meas.concat F m m'✝)) (MeasureSet.tainted m✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m✝¹dwi { 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m.last i m'✝

MeasRender F (Doc.concat d_left d_right) c i (Meas.concat F m m'✝)constructor
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m.last i m'✝

h₁
MeasRender F d_left c i ?m₁
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m.last i m'✝

h₂
MeasRender F d_right ?m₁.last i ?m₂
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m.last i m'✝

h
Meas.concat F m m'✝ = Meas.concat F ?m₁ ?m₂
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m.last i m'✝

m₁
Meas
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

m, m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

m'✝: Meas

h_current: Resolve F d₂ m.last i (MeasureSet.tainted m'✝)

h_transfer: m ∈ orig_ms

d_left: Doc

left✝¹: d_left ∈ L₁

h₁: MeasRender F d_left c i m

d_right: Doc

left✝: d_right ∈ L₂

h₂: MeasRender F d_right m.last i m'✝

m₂
Meas }
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝: List Meas

msr: MeasureSet

m✝: Meas

msr': MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝ :: ms✝ → x ∈ orig_ms

h_rest: ResolveConcat F ms✝ d₂ i msr

h_current: ResolveConcatOne F d₂ m✝ i msr'

h_ml: MeasureSet.tainted m = MeasureSet.union F msr' msr

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcase set => 
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝¹: List Meas

m✝: Meas

msr': MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝ :: ms✝¹ → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m✝ i msr'

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F msr' (MeasureSet.set ms✝ h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i mcases 
msr': MeasureSet
msr'
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝¹: List Meas

m✝¹: Meas

h_transfer: ∀ (x : Meas), x ∈ m✝¹ :: ms✝¹ → x ∈ orig_ms

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

m✝: Meas

h_current: ResolveConcatOne F d₂ m✝¹ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝²: List Meas

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ m✝ :: ms✝² → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F ms✝² d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m✝ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms✝¹ h✝¹)

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝¹: List Meas

m✝: Meas

msr': MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝ :: ms✝¹ → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m✝ i msr'

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F msr' (MeasureSet.set ms✝ h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m<;>
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝¹: List Meas

m✝¹: Meas

h_transfer: ∀ (x : Meas), x ∈ m✝¹ :: ms✝¹ → x ∈ orig_ms

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

m✝: Meas

h_current: ResolveConcatOne F d₂ m✝¹ i (MeasureSet.tainted m✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms✝ h✝)

tainted
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝²: List Meas

m✝: Meas

h_transfer: ∀ (x : Meas), x ∈ m✝ :: ms✝² → x ∈ orig_ms

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_rest: ResolveConcat F ms✝² d₂ i (MeasureSet.set ms✝¹ h✝¹)

ms✝: List Meas

h✝: ms✝ ≠ []

h_current: ResolveConcatOne F d₂ m✝ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms✝¹ h✝¹)

set
∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i m 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

m: Meas

d₁: Doc

L₁, L₂: List Doc

c: ℕ

orig_ms: List Meas

h_non_empty: orig_ms ≠ []

h_widen₁: Widen d₁ L₁

h_widen₂: Widen d₂ L₂

h_left: Resolve F d₁ c i (MeasureSet.set orig_ms h_non_empty)

ms✝¹: List Meas

m✝: Meas

msr': MeasureSet

h_transfer: ∀ (x : Meas), x ∈ m✝ :: ms✝¹ → x ∈ orig_ms

h_current: ResolveConcatOne F d₂ m✝ i msr'

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_ml: MeasureSet.tainted m = MeasureSet.union F msr' (MeasureSet.set ms✝ h✝)

∃ d_choiceless,
  d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂) L₁) ∧     MeasRender F d_choiceless c i msimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union] at 
h_ml: MeasureSet.tainted m = MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms✝¹ h✝¹)
h_ml
Goals accomplished! 🐙 
end
termination_by 
  ResolveConcat_tainted_valid => (
d₁: Doc
d₁.
size: Doc → ℕ
size + 
d₂: Doc
d₂.
size: Doc → ℕ
size + 
1: ?m.597808
1, 
0: ?m.597886
0, 
ms: List Meas
ms.
length: {α : Type ?u.597896} → List α → ℕ
length)
  Resolve_tainted_valid => (
d: Doc
d.
size: Doc → ℕ
size, 
1: ?m.597422
1, 
0: ?m.597433
0)